Practice
Solving Word Problems with Equations Practice
Fifty original questions covering totals, profit, distance-rate-time, round trips, capacities, sequential changes, and multi-step equations.
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Question 1
Explanation
Define the requested item count or per-item amount as the variable. Total value equals number of items times value per item, so \(7b=196\) and the answer is \(28\).
Question 2
Explanation
Define the requested item count or per-item amount as the variable. Total value equals number of items times value per item, so \(9(12)=108\) and the answer is \(108\).
Question 3
Explanation
Define the requested item count or per-item amount as the variable. Total value equals number of items times value per item, so \(12t=864\) and the answer is \(72\).
Question 4
Explanation
Define the requested item count or per-item amount as the variable. Total value equals number of items times value per item, so \(15m=525\) and the answer is \(35\).
Question 5
Explanation
Define the requested item count or per-item amount as the variable. Total value equals number of items times value per item, so \(8b=376\) and the answer is \(47\).
Question 6
Explanation
Let \(x\) be the original or sold quantity. Revenue is \(11(x-4)\), cost is \(5x\), and profit equals revenue minus cost. Solving \(11(x-4)-(5x)=100\) gives \(x=24\).
Question 7
Explanation
Let \(x\) be the original or sold quantity. Revenue is \(15(x-5)\), cost is \(8x\), and profit equals revenue minus cost. Solving \(15(x-5)-(8x)=128\) gives \(x=29\).
Question 8
Explanation
Let \(x\) be the original or sold quantity. Revenue is \(8x\), cost is \(120+3x\), and profit equals revenue minus cost. Solving \(8x-(120+3x)=280\) gives \(x=80\).
Question 9
Explanation
Let \(x\) be the original or sold quantity. Revenue is \(10(x-10)\), cost is \(4x\), and profit equals revenue minus cost. Solving \(10(x-10)-(4x)=200\) gives \(x=50\).
Question 10
Explanation
Let \(x\) be the original or sold quantity. Revenue is \(14(x-8)\), cost is \(6x\), and profit equals revenue minus cost. Solving \(14(x-8)-(6x)=208\) gives \(x=40\).
Question 11
Explanation
Define distance, rate, and time with their units. Use the needed form of \(d=rt\): \(d=9(4)=36\) kilometers.
Question 12
Explanation
Define distance, rate, and time with their units. Use the needed form of \(d=rt\): \(r=132/3=44\) miles per hour.
Question 13
Explanation
Define distance, rate, and time with their units. Use the needed form of \(d=rt\): \(t=84/7=12\) seconds.
Question 14
Explanation
Define distance, rate, and time with their units. Use the needed form of \(d=rt\): \(d=32(2.5)=80\) nautical miles.
Question 15
Explanation
Define distance, rate, and time with their units. Use the needed form of \(d=rt\): \(r=10.5/0.75=14\) kilometers per hour.
Question 16
Explanation
Let \(d\) be distance in kilometers. Convert time when needed, then use \(d=rt\). The time is \(1.5\) hours, so the distance is \(90\) kilometers.
Question 17
Explanation
Let \(d\) be distance in kilometers. Convert time when needed, then use \(d=rt\). The time is \(0.75\) hours, so the distance is \(3.6\) kilometers.
Question 18
Explanation
Let \(d\) be distance in kilometers. Convert time when needed, then use \(d=rt\). The time is \(20/60=1/3\) hour, so the distance is \(6\) kilometers.
Question 19
Explanation
Let \(d\) be distance in kilometers. Convert time when needed, then use \(d=rt\). The time is \(50/60=5/6\) hour, so the distance is \(10\) kilometers.
Question 20
Explanation
Let \(d\) be distance in kilometers. Convert time when needed, then use \(d=rt\). The time is \(2.25\) hours, so the distance is \(162\) kilometers.
Question 21
Explanation
Let \(d\) be the one-way distance. The segment times are \(d/50\) and \(d/40\), so \(d/50+d/40=9\). Solving gives \(d=200\).
Question 22
Explanation
Let \(d\) be the one-way distance. The segment times are \(d/60\) and \(d/45\), so \(d/60+d/45=7\). Solving gives \(d=180\).
Question 23
Explanation
Let \(d\) be the one-way distance. The segment times are \(d/24\) and \(d/16\), so \(d/24+d/16=5\). Solving gives \(d=48\).
Question 24
Explanation
Let \(d\) be the one-way distance. The segment times are \(d/15\) and \(d/10\), so \(d/15+d/10=5\). Solving gives \(d=30\).
Question 25
Explanation
Let \(d\) be the one-way distance. The segment times are \(d/6\) and \(d/4\), so \(d/6+d/4=5\). Solving gives \(d=12\).
Question 26
Explanation
Define one unknown and express the related amount using it. The balancing relationship is \(x-x/4-300=900\). Solving and then reporting the requested quantity gives \(1600\).
Question 27
Explanation
Define one unknown and express the related amount using it. The balancing relationship is \(0.8x-480=1520\). Solving and then reporting the requested quantity gives \(2500\).
Question 28
Explanation
Define one unknown and express the related amount using it. The balancing relationship is \(3x/5=48\). Solving and then reporting the requested quantity gives \(80\).
Question 29
Explanation
Define one unknown and express the related amount using it. The balancing relationship is \(x+(x-140)=860\), where \(x\) is the winner's count. Solving and then reporting the requested quantity gives \(500\).
Question 30
Explanation
Define one unknown and express the related amount using it. The balancing relationship is \(x+(x+12)=96\), where \(x\) is the smaller count. Solving and then reporting the requested quantity gives \(54\).
Question 31
Explanation
Let the variable represent the original total or capacity when needed. Translate the current and changed amounts into \(3c/8=45\). Solving gives \(120\).
Question 32
Explanation
Let the variable represent the original total or capacity when needed. Translate the current and changed amounts into \(0.75s=360\). Solving gives \(480\).
Question 33
Explanation
Let the variable represent the original total or capacity when needed. Translate the current and changed amounts into \(9.5-2.4=7.1\). Solving gives \(7.1\).
Question 34
Explanation
Let the variable represent the original total or capacity when needed. Translate the current and changed amounts into \(x-18=2x/3\). Solving gives \(54\).
Question 35
Explanation
Let the variable represent the original total or capacity when needed. Translate the current and changed amounts into \(x/5+32=3x/5\). Solving gives \(80\).
Question 36
Explanation
Apply each contextual change to the current amount in the stated order. After taxes \(2000\) remains; housing is \(500\), leaving \(1500\). The final requested amount is \(1500\).
Question 37
Explanation
Apply each contextual change to the current amount in the stated order. The discounted cost is \(0.75(120)=90\), then add \(8\). The final requested amount is \(98\).
Question 38
Explanation
Apply each contextual change to the current amount in the stated order. After the percentage loss \(680\) remains; then \(680-60=620\). The final requested amount is \(620\).
Question 39
Explanation
Apply each contextual change to the current amount in the stated order. After the first expense \(630\) remains; half of that is \(315\). The final requested amount is \(315\).
Question 40
Explanation
Apply each contextual change to the current amount in the stated order. Morning shipment is \(160\); total shipped is \(250\), leaving \(390\). The final requested amount is \(390\).
Question 41
Explanation
Let \(x\) be the relevant original or sold quantity. Write all revenue and all costs before using profit: \(9x-(240+3x)=480\). Solving gives \(x=120\).
Question 42
Explanation
Let \(x\) be the relevant original or sold quantity. Write all revenue and all costs before using profit: \(16(x-8)-7x=296\). Solving gives \(x=40\).
Question 43
Explanation
Let \(x\) be the relevant original or sold quantity. Write all revenue and all costs before using profit: \(11x-(150+5x)=270\). Solving gives \(x=70\).
Question 44
Explanation
Let \(x\) be the relevant original or sold quantity. Write all revenue and all costs before using profit: \(13(x-5)-4x=275\). Solving gives \(x=40\).
Question 45
Explanation
Let \(x\) be the relevant original or sold quantity. Write all revenue and all costs before using profit: \(18x-(360+6x)=600\). Solving gives \(x=80\).
Question 46
Explanation
Define the requested quantity and organize each segment or stage separately. The van's head start is \(48(0.5)=24\) miles; solve \(60t=48t+24\). Therefore the answer is \(2\).
Question 47
Explanation
Define the requested quantity and organize each segment or stage separately. Total distance is \(240\); times are \(3\) and \(2\) hours, so \(240/5=48\). Therefore the answer is \(48\).
Question 48
Explanation
Define the requested quantity and organize each segment or stage separately. Convert to \(135\) minutes and compute \(18(135)=2430\). Therefore the answer is \(2430\).
Question 49
Explanation
Define the requested quantity and organize each segment or stage separately. Travel times are \(0.5\) and \(0.5\) hour; add the \(0.25\)-hour rest. Therefore the answer is \(1.25\).
Question 50
Explanation
Define the requested quantity and organize each segment or stage separately. It starts with \(36\) liters, needs \(54\) more, and \(54/6=9\). Therefore the answer is \(9\).
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Questions to review
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- Question 1Total value equationsEasy
- Question 2Total value equationsEasy
- Question 3Total value equationsEasy
- Question 4Total value equationsEasy
- Question 5Total value equationsEasy
- Question 6Profit equationsEasy
- Question 7Profit equationsEasy
- Question 8Profit equationsEasy
- Question 9Profit equationsEasy
- Question 10Profit equationsEasy
- Question 11Distance rate timeEasy
- Question 12Distance rate timeEasy
- Question 13Distance rate timeEasy
- Question 14Distance rate timeEasy
- Question 15Distance rate timeEasy
- Question 16Rate table interpretationMedium
- Question 17Rate table interpretationMedium
- Question 18Rate table interpretationMedium
- Question 19Rate table interpretationMedium
- Question 20Rate table interpretationMedium
- Question 21Equal-distance round tripsMedium
- Question 22Equal-distance round tripsMedium
- Question 23Equal-distance round tripsMedium
- Question 24Equal-distance round tripsMedium
- Question 25Equal-distance round tripsMedium
- Question 26Budget and total equationsMedium
- Question 27Budget and total equationsMedium
- Question 28Budget and total equationsMedium
- Question 29Budget and total equationsMedium
- Question 30Budget and total equationsMedium
- Question 31Capacity and remaining quantityMedium
- Question 32Capacity and remaining quantityMedium
- Question 33Capacity and remaining quantityMedium
- Question 34Capacity and remaining quantityMedium
- Question 35Capacity and remaining quantityMedium
- Question 36Sequential quantity changesMedium
- Question 37Sequential quantity changesMedium
- Question 38Sequential quantity changesMedium
- Question 39Sequential quantity changesMedium
- Question 40Sequential quantity changesMedium
- Question 41Multi-step profit equationsHard
- Question 42Multi-step profit equationsHard
- Question 43Multi-step profit equationsHard
- Question 44Multi-step profit equationsHard
- Question 45Multi-step profit equationsHard
- Question 46Challenging equation applicationsHard
- Question 47Challenging equation applicationsHard
- Question 48Challenging equation applicationsHard
- Question 49Challenging equation applicationsHard
- Question 50Challenging equation applicationsHard