SOLUTION: 5. A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit? thanks.

Algebra ->  Equations -> SOLUTION: 5. A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit? thanks.      Log On


   



Question 184486: 5.
A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?
thanks.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the price of oranges be a
Let the price of lemons be b
given:
(1) 3a+%2B+5b+=+1026 (in cents)
(2) 6a+%2B+4b+=+1116 (in cents)
First, I will multiply both sides of (1) by 4
and both sides of (2) by 5
(1) 12a+%2B+20b+=+4104
(2) 30a+%2B+20b+=+5580
Now subtract (1) from (2)
(2) 30a+%2B+20b+=+5580
(1) -12a+-+20b+=+-4104
(3) 18a+=+1476
(3) a+=+82
Now plug this back into either equation to find b
(1) 3a+%2B+5b+=+1026
(1) 3%2A82+%2B+5b+=+1026
(1) 246+%2B+5b+=+1026
(1) 5b+=+780
(1) b+=+156
The price of oranges is 82 cents each. Thw price of
lemons is $1.56 each
check answers:
(1) 3a+%2B+5b+=+1026
(1) 3%2A82+%2B+5%2A156+=+1026
(1) 246+%2B+780+=+1026
(1) 1026+=+1026
(2) 6a+%2B+4b+=+1116
(2) 6%2A82+%2B+4%2A156+=+1116
(2) 492+%2B+624+=+1116
(2) 1116+=+1116
OK