Question

F almonds sell for $1.20 per pound, and walnuts sell for $.75 per pound, how many pounds of each must be used to make 45 pounds of a mixture to sell for $1.00 per pound?
A) 20 pounds of walnuts and 25 pounds of almonds

B) 25 pounds of walnuts and 20 pounds of almonds

C) 10 pounds of walnuts and 35 pounds of almonds

D) 35 pounds of walnuts and 10 pounds of almonds

Answer 1

Answer:

Option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.

Step-by-step explanation:

i) let x be the the number of pounds of almonds

ii) let y be the number of pounds of walnuts

iii) therefore x + y = 45 pounds of the mixture

iv) 1.2x + 0.75y = 1.00 $\times$ 45 = 45

v) Multipling equation in iv) by 4 we get

  4.8x + 3y = 180

vi) multiplying equation in iii) by 3 we get

     3x + 3y = 135

vii) subtracting equation vi) from equation v)  we get 1.8x = 45

ix) therefore we get x = 45/1.8 = 25 pounds of almonds

x) therefore 25 + y = 45  .... substituting value of x from ix) in iii) we get

   therefore y = 20 pounds of walnuts

Therefore option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.