Question

a Gerardo and Natalie are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Gerardo sold 16 small boxes of fruit and 14 large boxes of fruit for a total of $343.00. Natalie sold 13 small boxes of fruit and 23 large boxes of fruit for a total of $470.50. Find the cost of one small box of fruit and the cost of one large box of fruit. Cost of small box: $ Cost of large box: ​

Answer 1

Explanation:

x = cost of a small box

y = cost of a large box

16x + 14y =343

13x + 23y = 470.5

now we multiply both equations with factors so that we have the same number of x in both (we could the same for y, but I simply picked x, because their original factors are closer and smaller).

and then we subtract the second equation from the first and since the result for y.

13 × (16x + 14y = 343)

16 × (13x + 23y = 470.5)

gives us

208x + 182y = 4459

- 208x + 368y = 7528

----------------------------------

0x - 186y = -3069

186y = 3069

y = $16.50

now let's pick e.g. the first original equation to get x :

16x + 14y = 343

16x + 14×16.5 = 343

16x + 231 = 343

16x = 112

x = $7.00

the cost of a small box is $7.00

the cost of a large box is $16.50