MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The cost of each notebook is $5The cost of each thumb drive is $18Step-by-step explanation:We solve this problem by the system of equationsEquation for Troy and equation for Lisa and then solve the two equations simultaneous using the elimination methodAssume that the price of one notebook is $x and the price of onethumb drive is $yTroy 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 -4to eliminate x∵ 20 x + 65 y = 1270 ⇒ (3)∵ -20 x - 32 y = -676 ⇒ (4)Add equations (3) and (4)∴ 33 y = 594Divide both sides by 33∴ y = 18Substitute the value of y in equation (1) or (2) to find x∴ 4 x + 13(18) = 254∴ 4 x + 234 = 254Subtract 234 from both sides∴ 4 x = 20Divide both sides by 4∴ x = 5 x represents the cost per notebook and y represents the cost per thumb driveThe cost of each notebook is $5The cost of each thumb drive is $18