Question

A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?

A. 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
B. 8 lbs peanuts, 1 lb almonds, 2 lbs raisins
C. 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
D. 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

Answer 1

Answer:

C) 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins

Step-by-step explanation:

Your goal is to find out how many of each item will equate to 21 dollars. Your function is as follows:

1.5x+3y+1.5z=21

Where x, y, z are peanuts, almonds, raisins respectively (in that order). 21 is the total cost of the mixture.

All you have to do is start plugging in the variables given in the answer choices.

A) Peanuts (x) = 3, Almonds (y) = 6, Raisins (z) = 2

Everywhere you see x,y,z, you replace with their value.

$1.5x+3y+1.5z=21\\1.5(3)+3(6)+1.5(2)=21\\4.5+12+3=21\\\\19.5 \neq 21$

A doesn't equal 21. On to the next one.

B) Peanuts (x) = 8, Almonds (y) = 6, Raisins (z) = 2

Everywhere you see x,y,z, you replace with their value.

$1.5x+3y+1.5z=21\\1.5(8)+3(1)+1.5(2)=21\\12+3+3=21\\\\18 \neq 21$

B also doesn't equal 21. On to the next one...

C) Peanuts (x) = 6, Almonds (y) = 3, Raisins (z) = 2

Everywhere you see x,y,z you replace with their value.

$1.5x+3y+1.5z=21\\1.5(6)+3(3)+1.5(2)=21\\9+9+3=21\\\\\\21 = 21$

Both sides of the equation equal 21 which means C is our answer.