help with word problem

Question

A fruit stand sold 35 bags of fruit in one afternoon. Oranges sell for $10 per bag and Grapefruits sell for $12.50 a bag. Total money made was $425.00. How many of each bag were sold?

Answer 1

Let r = oranges and g = grapefruits

Here's what we know:

r + g = 35

10r + 12.5g = 425

 

We can solve this by substitution by isolating one of the variables in the first equation, or we can solve by elimination by multiplying the first equation by -10 and removing r. That's what I'll do in this case:

 

-10r - 10g = -350

10r + 12.5g = 425

-----------------------

2.5g = 75

Divide both sides by 2.5:

g = 30

 

Now to solve for r:

r + 30 = 35

r = 5

 

Now to check our answers:

 

10 * 5 + 12.5 * 30 = 425

50 + 375 = 425

425 = 425