Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought 4 notebooks and 13 thumb drives for $254. Lisa bought 5 notebooks and 8 thumb drives for $169. Find the cost of each notebook and each thumb drive.

The cost of each notebook is $5

The cost of each thumb drive is $18

Step-by-step explanation:

We solve this problem by the system of equations

Equation for Troy and equation for Lisa and then solve the two

equations simultaneous using the elimination method

Assume that the price of one notebook is $x and the price of one

thumb drive is $y

Troy bought 4 notebooks and 13 thumb drives for $254

∴ 4 x + 13 y = 254 ⇒ (1)

Lisa bought 5 notebooks and 8 thumb drives for $169

∴ 5 x + 8 y = 169 ⇒ (2)

To solve the equation multiply equation (1) by 5 and equation (2) by - 4

to eliminate x

∵ 20 x + 65 y = 1270 ⇒ (3)

∵ - 20 x - 32 y = - 676 ⇒ (4)

Add equations (3) and (4)

∴ 33 y = 594

Divide both sides by 33

∴ y = 18

Substitute the value of y in equation (1) or (2) to find x

∴ 4 x + 13 (18) = 254

∴ 4 x + 234 = 254

Subtract 234 from both sides

∴ 4 x = 20

Divide both sides by 4

∴ x = 5

x represents the cost per notebook and y represents the cost per

thumb drive

The cost of each notebook is $5

The cost of each thumb drive is $18