Question

Derek unpacked 126 kilograms of grapefruits and lemons. The grapefruits came in 10-kilogram bags and the lemons came in 8-kilogram bags. In all, Derek unpacked 13 bags of fruit. How many bags of grapefruits and bags of lemons did he unpack?

Answer 1

11 bags of grapefruits; 2 bags of lemons

Explanation:

Create a system of equations.

Let x be the number of grapefruit bags. Let y be the number of lemon bags.

x + y = 13

10x + 8y = 126

Rearrange the first equation to solve for x:

x = 13 - y

Substitute x in for x in the second equation:

10(13 - y) + 8y = 126

130 - 10y + 8y = 126

-2y = -4

y = 2

Plug y back into the first equation to solve for x.

x = 13 - 2

x = 11