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denis23 [38]
3 years ago
8

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. 3lbs 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
Mathematics
2 answers:
arlik [135]3 years ago
8 0
Given: 11-pound mixture of peanuts, almonds, and raisins
Cost:
peanuts - 1.5 per pound
almonds - 3 per pound
raisins - 1.5 per pound

mixture:
twice as many peanuts as almond; total cost of mixture is 21.

a + p + r = 11 lbs
a + 2a + r = 11 lbs
3a + r = 11
r = 11 - 3a

1.5(2a) + 3a + 1.5r = 21
3a + 3a + 1.5r = 21
6a + 1.5r = 21
6a + 1.5(11-3a) = 21
6a + 16.5 - 4.5a = 21
6a - 4.5a = 21 - 16.5
1.5a = 4.5
1.5a/1.5 = 4.5/1.5
a = 3

almonds = 3 lbs
peanuts = 2a = 2(3) = 6lbs
raisins = 11 - 3a = 11 - 3(3) = 11 - 9 = 2 lbs

<span>My answer is: C. 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins </span>
emmasim [6.3K]3 years ago
6 0

Let

x--------> pounds of peanuts

y--------> pounds of almonds

z--------> pounds of raisins

we know that

x+y+z=11 -----> equation 1

1.5x+3y+1.5z=21 -----> equation 2

x=2y -----> equation 3

Substitute the equation 3 in equation 1 and equation 2

So

[2y]+y+z=11

3y+z=11 -------> equation 4

1.5[2y]+3y+1.5z=21

3y+3y+1.5z=21

6y+1.5z=21 -----> equation 5

Solve the system

3y+z=11 -----> equation 4

6y+1.5z=21 -----> equation 5

Multiply by -2 equation 4

-6y-2z=-22

Adds equation 4 and equation 5

-6y-2z=-22\\ 6y+1.5z=21\\ --------\\ -0.5z=-1\\ z=2lb

find the value of y

6y+1.5z=21\\ 6y+1.5*2=21\\ 6y=21-3\\ y=18/6\\ y=3lb

find the value of x

x=2y\\ x=2*3\\ x=6lb

therefore

the answer is the option

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

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