Grade 9 · Algebra & functions

Linear system word problems practice

Linear system word problems is a grade 9 math skill aligned to Common Core standard HSA.REI.C.6: solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 linear system word problems problems our math games drill.

CCSS HSA.REI.C.610 questions in the bank
Sample questions

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Question 1easy

At a cafe, burgers cost bb dollars each and fries cost ff dollars each. One order of 44 burgers and 33 orders of fries cost $30\text{\char36}30. Another order of 22 burgers and 55 orders of fries cost $22\text{\char36}22. What is the price of one order of fries?

The system is 4b+3f=304b + 3f = 30 and 2b+5f=222b + 5f = 22. Double the second equation: 4b+10f=444b + 10f = 44. Subtract the first: 7f=147f = 14, so f=2f = 2.

Question 2easy

A snack bar sells large drinks for LL dollars each and small drinks for SS dollars each. One purchase of 22 large drinks and 33 small drinks cost $19\text{\char36}19. Another purchase of 44 large drinks and 11 small drink cost $23\text{\char36}23. What is the price of one small drink?

The system is 2L+3S=192L + 3S = 19 and 4L+S=234L + S = 23. Double the first equation: 4L+6S=384L + 6S = 38. Subtract the second: 5S=155S = 15, so S=3S = 3.

Question 3easy

A garden store sells large planters for LL dollars each and small planters for SS dollars each. One customer bought 22 large planters and 33 small planters for $54\text{\char36}54. Another customer bought 11 large planter and 55 small planters for $55\text{\char36}55. What is the price of one small planter?

The system is 2L+3S=542L + 3S = 54 and L+5S=55L + 5S = 55. Double the second equation: 2L+10S=1102L + 10S = 110. Subtract the first: 7S=567S = 56, so S=8S = 8.

Question 4medium

At a fruit stand, apples cost aa dollars per pound and oranges cost oo dollars per pound. One customer bought 44 pounds of apples and 22 pounds of oranges for $14\text{\char36}14. Another customer bought 22 pounds of apples and 55 pounds of oranges for $19\text{\char36}19. What is the price of one pound of oranges?

The system is 4a+2o=144a + 2o = 14 and 2a+5o=192a + 5o = 19. Double the second equation: 4a+10o=384a + 10o = 38. Subtract the first: 8o=248o = 24, so o=3o = 3.

Question 5medium

A bakery sells muffins for mm dollars each and cookies for cc dollars each. One customer bought 33 muffins and 55 cookies for $22\text{\char36}22. Another customer bought 22 muffins and 22 cookies for $12\text{\char36}12. What is the price of one muffin?

The system is 3m+5c=223m + 5c = 22 and 2m+2c=122m + 2c = 12. Divide the second equation by 22: m+c=6m + c = 6, so c=6mc = 6 - m. Substitute into the first: 3m+5(6m)=223m + 5(6 - m) = 22, so 3m+305m=223m + 30 - 5m = 22, 2m=8-2m = -8, and m=4m = 4.

Question 6medium

A camp sells senior passes for ss dollars each and junior passes for jj dollars each. One group bought 22 senior passes and 44 junior passes for $50\text{\char36}50. Another group bought 33 senior passes and 11 junior pass for $40\text{\char36}40. What is the price of one junior pass?

The system is 2s+4j=502s + 4j = 50 and 3s+j=403s + j = 40. From the second equation, j=403sj = 40 - 3s. Substitute into the first: 2s+4(403s)=502s + 4(40 - 3s) = 50, so 2s+16012s=502s + 160 - 12s = 50, 10s=110-10s = -110, s=11s = 11, and j=7j = 7.

Question 7medium

A print shop charges cc dollars per color copy and bb dollars per black-and-white copy. One order of 55 color copies and 22 black-and-white copies cost $12\text{\char36}12. Another order of 22 color copies and 66 black-and-white copies cost $10\text{\char36}10. What is the price of one black-and-white copy?

The system is 5c+2b=125c + 2b = 12 and 2c+6b=102c + 6b = 10. Multiply the first equation by 33: 15c+6b=3615c + 6b = 36. Subtract the second: 13c=2613c = 26, so c=2c = 2. Then 2(2)+6b=102(2) + 6b = 10, 6b=66b = 6, and b=1b = 1.

Question 8medium

A clothing shop sells long-sleeve shirts for ll dollars each and short-sleeve shirts for ss dollars each. One purchase of 22 long-sleeve shirts and 33 short-sleeve shirts cost $49\text{\char36}49. Another purchase of 44 long-sleeve shirts and 11 short-sleeve shirt cost $53\text{\char36}53. What is the price of one long-sleeve shirt?

The system is 2l+3s=492l + 3s = 49 and 4l+s=534l + s = 53. Double the first equation: 4l+6s=984l + 6s = 98. Subtract the second: 5s=455s = 45, so s=9s = 9. Then 4l+9=534l + 9 = 53, 4l=444l = 44, and l=11l = 11.

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