Question

POSSIBLE POINTS 6.67

Jacob made two trips to the store. On his first trip to the store, he
bought x kitchen towels for $3 each and y dishcloths for $2 each and spent
a total of $32. On his second trip to the store, he bought x oven mitts for $5
each and returned the y dishcloths he bought on the first trip. He was
refunded the money for the dishcloths and still spent $32. The system of
equations shown below represents the amounts, in dollars, he spent on the
two trips to the store.
3x + 2y = 32
5x - 2y = 32
How many kitchen towels and dishcloths did Jacob buy on his first trip to the
store?
o 10 kitchen towels and 4 dishcloths
o 4 kitchen towels and 10 dishcloths
04 kitchen towels and 8 dishcloths
8 kitchen towels and 4 dishcloths

Answer 1

8 kitchen towels and 4 dishcloths!

Explanation:

first equation is 3x + 2y = 32

second equation is 5x - 2y = 32

add the two equations together to get 8x = 64

solve for x to get x = 64 / 8 = 8

replace x with 8 in the first equation to get 24 + 2y = 32

solve for y to get y = 8/2 = 4

you have x = 8 and y = 4

first equation becomes 24 + 8 = 32

second equation becomes 40 - 8 = 32

the solution checks out ok.

solution is x = 8 and y = 2 which means he bought 8 kitchen towels and 4 dishcloths on his first trip.