Respuesta :
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
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
