Question

A grocer mixed pecans worth $0.84 per pound with cashews worth $1.40 per pound. If he made 88 pounds of a mixture worth $1.26 per pound, how many pounds of pecans are in the mixture?

Answer 1

Answer: the mixture contained 22 pounds of pecans

Step-by-step explanation:

Let x represent the number of pounds of pecans in the mixture.

Let y represent the number of pounds of cashews in the mixture.

The grocer made 88 pounds of the mixture. This means that

x + y = 88

If the mixture is worth $1.26 per pound, it means that the total cost of the mixture that he made would be

88 × 1.26 = $110.88

The grocer mixed pecans worth $0.84 per pound with cashews worth $1.40 per pound. This means that

0.84x + 1.4y = 110.88 - - - - - - - - - - 1

Substituting x = 88 - y into equation 1, it becomes

0.84(88 - y) + 1.4y = 110.88

73.92 - 0.84y + 1.4y = 110.88

- 0.84y + 1.4y = 110.88 - 73.92

0.56y = 36.96

y = 36.96/0.56

y = 66

x = 88 - y = 88 - 66

x = 22

Answer 2

Answer:

There are 22 pounds of pecans in the mixture

Step-by-step explanation:

Let the number of pounds of pecans be p and the number of cashews be c

We have 88 pounds in total, mathematically, this means;

c + p = 88

Now, the 88 mixtures cost $1.4 per pounds. This means the total amount of the 88 would be 88 * 1.26= $110.88

The pecans are worth 0.84 per pound while the cashews are worth 1.4 per pound. If the total is at a cost of 110.88, this can be translated mathematically as:

0.84p + 1.4c = 110.88

We now have two different equations that we can solve simultaneously.

c + p = 88

0.84p + 1.4c = 110.88

From the first equation, we can say c = 88 - p

We can then substitute the into the second equation:

0.84p + 1.4(88 - p) = 110.88

0.84p + 123.2 - 1.4p = 110.88

-0.56p = 110.88 - 123.2

0.56p = 12.32

p = 12.32/0.56 = 22

Now, we know c = 88 - p = 88 - 22 = 66