Arthimetic simple question?? HELP

Question

John brought 4 pounds of almonds for a total of cost of $22

THe cost per pound for cashews is 60% MORE than the cost per pound for almonds.

 

john bought enough cashews taht, when he mixed them with the almonds, the mixture had a value of $6.50 per pound?

Aproximatelywhat percent of the mixture, by wieght was cashews?

 

 

Answer 1

4a = 22

a = 22 / 4

a = 5.5 (almonds cost $5.50 per pound)

 

5.5 * 1.6 = 8.8 (cashews cost $8.8)

 

5.5 * 4 + 8.8c

----------------   = 6.5

      4 + c

 

22 + 8.8c = 6.5(4 + c)

8.8c + 22 = 6.5c + 26

2.3c + 22 = 26

2.3c = 4

c ≈ 1.74

 

So there's about 1.74 pounds of cashews.

1.74 + 4 = 5.74 (total poundage)

1.74 / 5.74 ≈ .3031

Move the decimal two spaces over:

30.31%

Answer 2

Let A be the cost per pound of almonds

Then A = $22/4 = $5.5

 

Let C be the cost per pound of cashews

Then C = 1.6A = 1.6*($5.5) = $8.8

 

Let 'a' be the pounds of almonds bought and let 'c' be the pounds of cashews bought

(5.5a + 8.8c)/(a+c) = 6.5

5.5a + 8.8c = 6.5a + 6.5c

a = 2.3c

 

Percent weight of cashews = c/(a+c) x 100% = c/(2.3c + c) x 100% = c/3.3c x 100% = 30.3%