you picked 50 bushels of fruit and you spend $120 with apples costing $2 per bushel and oranges $3 per bushel how many bushels of each fruit did you pick?

Question

write a system of equations

Answer 1

You picked 50 total bushels, some apples, and some oranges. Let's call them P for apples and R for oranges

 

P+R=50

 

You paid $2 per bushel of apples and $3 per bushel of oranges, totalling $120

 

2P+3R=120

 

Now we have a system of equations:

 

P+R=50

2P+3R=120

 

I'm going to use elimination by multiplication. I'm going to multiply my first equation by two, then subtract it from my second equation. That way, I see that my P variable will be cancelled out:

 

2P+2R=100

2P+3R=120

 

1R=20

R=20 bushels

 

If I picked 20 bushels of oranges, I must have picked 30 bushels of apples. I can also double check this by plugging it back in to my other equation:

 

$2(30)+$3(20)

$60+$60

$120