Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Johanna bought 19 items at the college bookstore. The items cost a total of 
$35.50. The pens cost 
$0.50 each, the notebooks were 
$3.00 each, and the highlighters cost 
$1.50 each. She bought 2 more notebooks than highlighters. How many of each item did she buy?
Use a system of three linear equations to solve the problem.

Johanna bought 1919 items at the college bookstore. The items cost a total of $35.50 \$ 35.50 . The pens cost $0.50 \$ 0.50 each, the notebooks were $3.00 \$ 3.00 each, and the highlighters cost $1.50 \$ 1.50 each. She bought 22 more notebooks than highlighters. How many of each item did she buy?\newlineUse a system of three linear equations to solve the problem.

Full solution

Q. Johanna bought 1919 items at the college bookstore. The items cost a total of $35.50 \$ 35.50 . The pens cost $0.50 \$ 0.50 each, the notebooks were $3.00 \$ 3.00 each, and the highlighters cost $1.50 \$ 1.50 each. She bought 22 more notebooks than highlighters. How many of each item did she buy?\newlineUse a system of three linear equations to solve the problem.
  1. Define variables for items: Define variables for each type of item Johanna bought: let pp be the number of pens, nn be the number of notebooks, and hh be the number of highlighters. Johanna bought a total of 1919 items.
  2. Set up total cost equation: Set up the total cost equation using the prices given for each item. Pens cost $0.50\$0.50 each, notebooks $3.00\$3.00 each, and highlighters $1.50\$1.50 each. The total cost of all items is $35.50\$35.50.
  3. Express relationship between notebooks and highlighters: Johanna bought 22 more notebooks than highlighters. This relationship can be expressed as an equation.
  4. Substitute equations to reduce variables: Substitute the equation from step 33 into the equations from steps 11 and 22 to reduce the number of variables. Replace nn with (h+2)(h + 2) in both equations.
  5. Simplify equations: Simplify the equations obtained in step 44.
  6. Further simplify and rearrange: Further simplify and rearrange the equations.
  7. Solve for number of pens: Solve one of the equations for pp. From the first simplified equation, express pp in terms of hh.
  8. Substitute pen expression into equation: Substitute the expression for pp from step 66 into the second simplified equation.
  9. Distribute and combine terms: Distribute and combine like terms in the equation from step 77.
  10. Solve for highlighters: Solve for hh.

More problems from Solve a system of equations using elimination: word problems