Question

Kristen went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her coworkers. Boxes of chocolate cost $10 each and boxes of ornaments cost $7 each. She buys a total of 17 boxes and spends $146. How many boxes of chocolates and how many boxes of ornaments does she buy?

a) 9 boxes of chocolates, 8 boxes of ornaments
b) 8 boxes of chocolates, 9 boxes of ornaments
c) 10 boxes of chocolates, 7 boxes of ornaments
d) 7 boxes of chocolates, 10 boxes of ornaments

Answer 1

Kristen bought 9 boxes of chocolates and 8 boxes of ornaments.

Step-by-step explanation:

Let's represent the number of boxes of chocolates as x and the number of boxes of ornaments as y.

We have two equations based on the given information:

Equation 1: x + y = 17 (the total number of boxes)

Equation 2: 10x + 7y = 146 (the total cost of the boxes)

We can solve these equations using the substitution method:

1. Rewrite Equation 1 as x = 17 - y.
2. Substitute this value of x into Equation 2: 10(17 - y) + 7y = 146.
3. Distribute and simplify: 170 - 10y + 7y = 146.
4. Combine like terms: -3y = -24.
5. Divide both sides by -3 to solve for y: y = 8.
6. Substitute this value of y back into Equation 1 to solve for x: x + 8 = 17. Hence, x = 9.

Therefore, Kristen bought 9 boxes of chocolates and 8 boxes of ornaments, so the answer is option a) 9 boxes of chocolates, 8 boxes of ornaments.