SOLUTION: three apples and five grapes cost $1.70; five apples and three grapes cost $2.46. What is the cost of one grape?

Algebra ->  Human-and-algebraic-language -> SOLUTION: three apples and five grapes cost $1.70; five apples and three grapes cost $2.46. What is the cost of one grape?      Log On


   



Question 198128: three apples and five grapes cost $1.70; five apples and three grapes cost $2.46. What is the cost of one grape?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= the cost of 1 apple
Let g= the cost of 1 grape
given:
(1) 3a+%2B+5g+=+170 (in cents)
(2) 5a+%2B+3g+=+246 (in cents)
Multiply both sides of (1) by 5
Multiply both sides of (2) by 3
Subtract (2) from (1)
(1) 15a+%2B+25g+=+850
(2) -15a+-+9g+=+-738
------------------------
16g+=+112
g+=+7
The cost of 1 grape is 7 cents
check answer:
3a+%2B+5%2A7+=+170
3a+%2B+35+=+170
3a+=+170+-+35
3a+=+135
a+=+45
and
5a+%2B+3g+=+246
5%2A45+%2B+3%2A7+=+246
225+%2B+21+=+246
246+=+246
OK