Question

Each week peggy drives two routes, route x and route y. One week she drives route x three times a d route y twice. She drives a total of 144 miles that week. Another week she drives route x twice and route y five times. She drives a total of 217 miles that week. Find the length of each route

Answer 1

x = 26 , y = 33

Explanation:

3x + 2y = 144 (1)

2x + 5y = 217 (2)

3x + 2y = 144

(divide the equation by 3)

x + (2/3)y = 48

x = 48 - (2/3)y

Plug into (2)

2[48 - (2/3)y] + 5y = 217

96 - (4/3)y + 5y = 217

11y/3 = 217 - 96

11y/3 = 121

y = 121×3/11

y = 33

x = 48 - (2/3)y

x = 48 - (2/3)(33)

x = 48 - 22

x = 26