Johanna bought 12 items at the college bookstore. The items cost a total of $29.00. The pens cost $0.50 each, the notebooks were $4.00 each, and the highlighters cost $1.50 each. She bought 4 more notebooks than highlighters. How many of each item did she buy? Use a system of three linear equations to solve the problem.

Question

Johanna bought 12 items at the college bookstore. The items cost a total of  $29.00. The pens cost  $0.50 each, the notebooks were  $4.00 each, and the highlighters cost  $1.50 each. She bought 4 more notebooks than highlighters. How many of each item did she buy? Use a system of three linear equations to solve the problem.

Bytelearn · Accepted Answer

Define variables:  Let's define the variables: let p be the number of pens, n be the number of notebooks, and h be the number of highlighters Johanna bought. Write first equation:  We know the total number of items bought is 12, so we write the first equation: p + n + h = 12. Write second equation:  The total cost of all items is $29.00. Each pen costs $0.50, each notebook costs $4.00, and each highlighter costs $1.50. We write the second equation based on the total cost: 0.50p + 4n + 1.50h = 29. Write third equation:  Johanna bought 4 more notebooks than highlighters, so we have the third equation: n = h + 4. Substitute third equation:  Substitute the third equation into the first and second equations. Replace n with h + 4 in the first equation: p + (h + 4) + h = 12. Simplify to get p + 2h + 4 = 12. Solve for p:  Solve for p: p = 12 - 2h - 4. Simplify further to get p = 8 - 2h. Substitute n into cost equation:  Now substitute n = h + 4 into the cost equation: 0.50p + 4(h + 4) + 1.50h = 29. This simplifies to 0.50p + 4h + 16 + 1.50h = 29. Substitute p into cost equation:  Substitute p = 8 - 2h into the equation: 0.50(8 - 2h) + 4h + 16 + 1.50h = 29. Simplify to get 4 - h + 4h + 16 + 1.50h = 29. Combine like terms:  Combine like terms: 4 + 5.50h + 16 = 29. Simplify to get 5.50h + 20 = 29. Solve for h:  Solve for h: 5.50h = 29 - 20. Simplify to get 5.50h = 9.  Divide by 5.50 to find h: h = 9 / 5.50. This gives h = 1.64, which doesn't make sense because the number of highlighters should be a whole number.

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