Practice
Solving Word Problems Using Systems of Equations Practice
Fifty original questions covering system setup, count/value tables, tickets, coins, inventory, object features, method choice, and feasibility.
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Question 1
Explanation
Define both variables exactly as stated. One equation records the total count or time, while the second multiplies each quantity by its own value or feature. This produces \(b+p=30,\ 6b+10p=220\).
Question 2
Explanation
Define both variables exactly as stated. One equation records the total count or time, while the second multiplies each quantity by its own value or feature. This produces \(n+d=24,\ 0.05n+0.10d=1.65\).
Question 3
Explanation
Define both variables exactly as stated. One equation records the total count or time, while the second multiplies each quantity by its own value or feature. This produces \(x+y=70,\ x-y=12\).
Question 4
Explanation
Define both variables exactly as stated. One equation records the total count or time, while the second multiplies each quantity by its own value or feature. This produces \(m+c=18,\ 2m+4c=50\).
Question 5
Explanation
Define both variables exactly as stated. One equation records the total count or time, while the second multiplies each quantity by its own value or feature. This produces \(a+b=8,\ 12a+18b=120\).
Question 6
Explanation
Define the two counts and translate the total and comparison separately: \(L+S=64\) and \(L-S=10\). Solving the system and selecting the requested count gives \(37\).
Question 7
Explanation
Define the two counts and translate the total and comparison separately: \(L+S=90\) and \(L=2S\). Solving the system and selecting the requested count gives \(60\).
Question 8
Explanation
Define the two counts and translate the total and comparison separately: \(x+y=52\) and \(y=x+8\). Solving the system and selecting the requested count gives \(22\).
Question 9
Explanation
Define the two counts and translate the total and comparison separately: \(A+B=75\) and \(A=B-15\). Solving the system and selecting the requested count gives \(45\).
Question 10
Explanation
Define the two counts and translate the total and comparison separately: \(U+L=48\) and \(U=3L\). Solving the system and selecting the requested count gives \(36\).
Question 11
Explanation
Let \(x\) be basic kit and \(y\) be advanced kit. Write \(x+y=50\) and \(7x+11y=430\). Solving gives \(y=20\).
Question 12
Explanation
Let \(x\) be standard voucher and \(y\) be premium voucher. Write \(x+y=60\) and \(5x+9y=420\). Solving gives \(y=30\).
Question 13
Explanation
Let \(x\) be day badge and \(y\) be full badge. Write \(x+y=45\) and \(8x+14y=450\). Solving gives \(y=15\).
Question 14
Explanation
Let \(x\) be small package and \(y\) be large package. Write \(x+y=40\) and \(12x+18y=570\). Solving gives \(y=15\).
Question 15
Explanation
Let \(x\) be seed bundle and \(y\) be tool bundle. Write \(x+y=32\) and \(6x+15y=246\). Solving gives \(y=6\).
Question 16
Explanation
Define the two ticket counts. The count and revenue relationships are \(r+p=80\), \(9r+14p=890\). Solving them together gives the requested higher-price count \(34\).
Question 17
Explanation
Define the two ticket counts. The count and revenue relationships are \(x+y=50\), \(6x+11y=380\). Solving them together gives the requested higher-price count \(16\).
Question 18
Explanation
Define the two ticket counts. The count and revenue relationships are \(x+y=120\), \(5x+8y=744\). Solving them together gives the requested higher-price count \(48\).
Question 19
Explanation
Define the two ticket counts. The count and revenue relationships are \(s+d=70\), \(4s+10d=430\). Solving them together gives the requested higher-price count \(25\).
Question 20
Explanation
Define the two ticket counts. The count and revenue relationships are \(x+y=90\), \(7x+12y=780\). Solving them together gives the requested higher-price count \(30\).
Question 21
Explanation
Use consistent cents throughout. The coin-count and value equations are \(d+q=40\), \(10d+25q=700\) cents. Solving gives the requested coin count \(20\).
Question 22
Explanation
Use consistent cents throughout. The coin-count and value equations are \(n+q=36\), \(5n+25q=480\) cents. Solving gives the requested coin count \(15\).
Question 23
Explanation
Use consistent cents throughout. The coin-count and value equations are \(d+h=30\), \(10d+50h=820\) cents. Solving gives the requested coin count \(13\).
Question 24
Explanation
Use consistent cents throughout. The coin-count and value equations are \(q+d=28\), \(25q+100d=1300\) cents. Solving gives the requested coin count \(8\).
Question 25
Explanation
Use consistent cents throughout. The coin-count and value equations are \(n+d=50\), \(5n+10d=360\) cents. Solving gives the requested coin count \(22\).
Question 26
Explanation
Let \(x\) count adapters and \(y\) count cables. Use \(x+y=35\) and \(18x+7y=410\). Solving gives \(x=15\).
Question 27
Explanation
Let \(x\) count large boxes and \(y\) count small boxes. Use \(x+y=42\) and \(14x+8y=444\). Solving gives \(x=18\).
Question 28
Explanation
Let \(x\) count rackets and \(y\) count balls. Use \(x+y=60\) and \(25x+5y=600\). Solving gives \(x=15\).
Question 29
Explanation
Let \(x\) count binders and \(y\) count folders. Use \(x+y=80\) and \(9x+3y=420\). Solving gives \(x=30\).
Question 30
Explanation
Let \(x\) count frames and \(y\) count canvases. Use \(x+y=46\) and \(16x+10y=580\). Solving gives \(x=20\).
Question 31
Explanation
The first equation counts objects; the second counts the feature per object. Using \(b+t=26\), \(2b+3t=62\) and solving gives \(10\) for the requested type.
Question 32
Explanation
The first equation counts objects; the second counts the feature per object. Using \(c+m=30\), \(4c+2m=102\) and solving gives \(21\) for the requested type.
Question 33
Explanation
The first equation counts objects; the second counts the feature per object. Using \(c+g=40\), \(2c+4g=112\) and solving gives \(16\) for the requested type.
Question 34
Explanation
The first equation counts objects; the second counts the feature per object. Using \(c+s=28\), \(4c+3s=100\) and solving gives \(16\) for the requested type.
Question 35
Explanation
The first equation counts objects; the second counts the feature per object. Using \(v+t=22\), \(4v+6t=104\) and solving gives \(8\) for the requested type.
Question 36
Explanation
Method and interpretation decisions follow equation structure and context. Substitution, because \(x=48-y\) is immediate.
Question 37
Explanation
Method and interpretation decisions follow equation structure and context. Elimination, because the \(y\)-coefficients are opposites.
Question 38
Explanation
Method and interpretation decisions follow equation structure and context. The second equation is only a multiple of the first.
Question 39
Explanation
Method and interpretation decisions follow equation structure and context. No, a system solution must satisfy both equations.
Question 40
Explanation
Method and interpretation decisions follow equation structure and context. The equations or supplied context are incompatible with a physical ticket count.
Question 41
Explanation
Define both quantities and translate the two independent relationships: \(s+p=125\), \(18s+27p=2655\). Solve the system, then match the requested label to obtain \(45\).
Question 42
Explanation
Define both quantities and translate the two independent relationships: \(o+y=68\), \(o-y=12\). Solve the system, then match the requested label to obtain \(40\).
Question 43
Explanation
Define both quantities and translate the two independent relationships: \(t+s=90\), \(3t+7s=438\). Solve the system, then match the requested label to obtain \(42\).
Question 44
Explanation
Define both quantities and translate the two independent relationships: \(x+y=19\), \(3x+5y=83\). Solve the system, then match the requested label to obtain \(13\).
Question 45
Explanation
Define both quantities and translate the two independent relationships: \(x+y=30\), \(4x+7y=156\). Solve the system, then match the requested label to obtain \(12\).
Question 46
Explanation
Use the supplied relationships or candidate pair and verify the context. The pair satisfies \(20+16=36\) and \(5(20)+9(16)=244\). The requested result is \(36\).
Question 47
Explanation
Use the supplied relationships or candidate pair and verify the context. \(d+c=34\), \(40d+25c=1045\). The requested result is \(13\).
Question 48
Explanation
Use the supplied relationships or candidate pair and verify the context. \(x+y=48\), \(6x+10y=352\). The requested result is \(16\).
Question 49
Explanation
Use the supplied relationships or candidate pair and verify the context. \(L+S=44\), \(L-S=8\). The requested result is \(18\).
Question 50
Explanation
Use the supplied relationships or candidate pair and verify the context. \(x+y=72\), \(15x+22y=1332\). The requested result is \(36\).
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Questions to review
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- Question 1Writing systems from contextEasy
- Question 2Writing systems from contextEasy
- Question 3Writing systems from contextEasy
- Question 4Writing systems from contextEasy
- Question 5Writing systems from contextEasy
- Question 6Count and comparison systemsEasy
- Question 7Count and comparison systemsEasy
- Question 8Count and comparison systemsEasy
- Question 9Count and comparison systemsEasy
- Question 10Count and comparison systemsEasy
- Question 11Quantity-value systems from tablesEasy
- Question 12Quantity-value systems from tablesEasy
- Question 13Quantity-value systems from tablesEasy
- Question 14Quantity-value systems from tablesEasy
- Question 15Quantity-value systems from tablesEasy
- Question 16Ticket revenue systemsMedium
- Question 17Ticket revenue systemsMedium
- Question 18Ticket revenue systemsMedium
- Question 19Ticket revenue systemsMedium
- Question 20Ticket revenue systemsMedium
- Question 21Coin systemsMedium
- Question 22Coin systemsMedium
- Question 23Coin systemsMedium
- Question 24Coin systemsMedium
- Question 25Coin systemsMedium
- Question 26Inventory systems from tablesMedium
- Question 27Inventory systems from tablesMedium
- Question 28Inventory systems from tablesMedium
- Question 29Inventory systems from tablesMedium
- Question 30Inventory systems from tablesMedium
- Question 31Object and feature systemsMedium
- Question 32Object and feature systemsMedium
- Question 33Object and feature systemsMedium
- Question 34Object and feature systemsMedium
- Question 35Object and feature systemsMedium
- Question 36System method and feasibilityMedium
- Question 37System method and feasibilityMedium
- Question 38System method and feasibilityMedium
- Question 39System method and feasibilityMedium
- Question 40System method and feasibilityMedium
- Question 41Multi-step contextual systemsHard
- Question 42Multi-step contextual systemsHard
- Question 43Multi-step contextual systemsHard
- Question 44Multi-step contextual systemsHard
- Question 45Multi-step contextual systemsHard
- Question 46System verification and interpretationHard
- Question 47System verification and interpretationHard
- Question 48System verification and interpretationHard
- Question 49System verification and interpretationHard
- Question 50System verification and interpretationHard