At the local grocer, 3 apples and 5 oranges cost total of $6.20. 7 apples and 4 oranges cost a total of $7.95. What is the cost of one apple and one orange?

Answer 1

Hello Nathalia,

Let A = # of apples and B = # of oranges.

Then we have

3A + 5B = 6.20 and 7A + 4B = 7.95.

Let's use the 'elimination method' by multiplying the first equations by -4, and the second one by 5.

Why? So that the B's will cancel when I add the two equaitons together. So, now we have

-12A - 20B = -24.80 and

35A + 20B = 39.75. Adding them together, we get

23A = 14.95

→ A = $.65.

Subsitute this back in to either of the original equaitons to get

B = $.85.

I hope the above helps, and thank you for the question. Have a great afternoon!

Michael E.

Answer 2

3x + 5y = 620

7x + 4y = 795

elimination: 4 times first equation and -5 times second equation:

12x + 20y = 2480

-35x + -20y = -3975

-23x = -1495

x= 65

apples cost 65 cents

3(65) + 5y = 620

195 + 5y = 620

5y = 425

y = 85

oranges cost 85 cents

CHECK

7(65) + 4(85) =

455 + 340 = 795

oranges cost 85 cents, apples cost 65 cents