store charges $2 for peanuts, $5 for raisins, and $3 for granola. You buy 60 lbs for $180. If you bought 10 more peanuts than granola, how many of each item did you buy?

Question

I don't understand the steps for this problem.

Answer 1

Let:

P = number of pounds of peanuts

R = number of pounds of raisins

G = number of pounds of granola

You buy 60 pounds:

P + R + G = 60 [eq1]

Note that (price per pound)*(number of pounds) = dollars for that item:

$2P + $5R + $3G = $180 [eq2]

Also, you bought 10 lbs more of peanuts than granola: P = 10 + G [eq3]

Plug [eq3] into [eq1]:

(10 + G) + R + G = 60

2G + R = 50 [eq4]

Plug [eq3] into [eq2]:

2(10+G) + 5R + 3G = 180

5G + 5R = 160 [eq5\

10G + 5R = 250 [eq4 * 5]

5G + 5R = 160 [eq5 again]

------------------------------ [elimination; subtract equations]

5G = 90

G = 18 pounds

From [eq3] P = 10 + G

P = 28 pounds

Now, remember [eq1]:

P + R + G = 60

28 + R + 18 = 60

R = 14 pounds

Check:

Does P + R + G = 60 ?

28 + 14 + 18 = 60 ?

60 = 60 ?yes

Does

$2P + $5R + $3G = $180 ?

$2(28) + $5(14) + $3(18) = $180 ?

$56 + $70 + $54 = $180 ?

$180 = $180 ?yes

Answer 2

brought 20-peanuts for 2 dollars = $40

brought 10- granola for 3 dollars = $30

brought 22- raisins for 5 dollars = $110

The question states you brought 10 more peanuts than granola but never states how much raisins are brought to complete the question 10 more peanuts have to brought than raisins which will mean he brought 20 peanuts after getting the amount for how much 20 peanuts and 10 granolas are worth you will get 70 and subtract 70 from 180 you get 110 then divide 110 by 5 too know how much raisins were brought