Question

13. Cost of Clay For his art class, Bryce bought 2 kilograms of dark clay and 3 kilograms of light clay, paying $22 for the clay. He later needed 1 kilogram of dark clay and 2 kilograms of light clay, which cost $13 altogether. What was the cost per kilogram for each type of clay?

Answer 1

Let x be the unit cost of the dark clay and y be the unit cost of the light clay

2x + 3y = $22 --------------------------------(1)

x + 2y = $13 ------------------------------------(2)

We can now solve the 2 simultaneous equation using the elimination method

multiply equation (1) b y 1 and multiply (2) by 2

2x + 3y = $22 -----------------------------------(3)

2x + 4y = $26 ------------------------------------(4)

subtract equation (3) from (4)

y = $4

substitute y=$4 into equation (2) and solve for x

x + 2y = $13

x + 2($4) = $13

x+ $8 = $13

subtract $8 from both-side of the equation

x - $8 = $13 - $8

x=$5

The dark clay cost $5 per kilogram and the light clay cost $4 per kilogram