Mathematics, 10.08.2021 22:40, briseidam6683

A candy store owner wants to mix some candy costing $1.25 a pound with some candy costing $1.45 a pound to make 50 pounds of candy
costing $1.30 a pound. How much of the $1.25 a pound candy should
she use?

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Answers

answered: maves8

The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.

Given:

Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a poundThe resulting mixture should be 50 pounds of candyThe resulting mixture should cost $1.30 a pound

To find: The amount of candy costing $1.25 a pound that should be mixed

Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.

Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with ' 50-x ' pounds of candy costing $1.45 a pound.

Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and ' 50-x ' pounds of candy costing $1.45 a pound.

Accordingly, the total cost of the resulting mixture is 1.25x+1.45(50-x)

However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is $1.30 \times 50$

Equating the total cost of the resulting mixture obtained in two ways, we get,

$1.25x+1.45(50-x)=1.30 \times 50$

1.25x+72.5-1.45x=65

0.2x=7.5

$x=\frac{7.5}{0.2}$

x=37.5

This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.

Learn more about cost of mixtures here:

answered: leannaadrian

When the candy costs $\bold{\$1.25}$ a pound, the candy store owner must use $\bold{37.5}$ pounds. $\bold{\$1.25}$ per-pound candy is to be blended with $\bold{\$1.45}$ per-pound candy.There must be $\bold{50\ pounds}$ of candy in the mixture So, the $\bold{\$1.30}$ per-pound ought to be the cost of a final mixture.This is the amount of $\bold{\$1.25}$ candy per pound which should be blended when 'x' pounds of candy cost $\bold{\$1.25}$ a pound, therefore the resultant combination must be constructed by joining 'x' pounds of candy together.The x pounds of candy costing $\bold{\$1.25}$ per pound must be combined with " $\bold{50-x}$ " pounds of candy costing $\bold{\$1.45}$ per pound because the total weight of its final mixture must be $\bold{50\ pounds}$ .Later, 'x' pounds of candy costing $\bold{\$1.25}$ per-pound is mixed with ' $\bold{50-x}$ ' pounds of candy costing $\bold{\$1.45}$ per pound to achieve the desired mixture. As a result, the overall total cost of the final mixture is: $\to \bold{1.25x+1.45(50-x)}$ A 50-pound batch of a mixture will cost $\bold{\$1.30}$ per pound, and As an outcome, your total cost of the resulting mixture is $\bold{1.30 \times 50}$ .It might calculate the overall cost of the resulting mixture by multiplying it by two.

$\to \bold{ 1.25x+1.45(50-x)= 1.30 \times 50}\\\\ \to \bold{ 1.25x+72.5-1.45x= 65}\\\\ \to \bold{ -0.2x= -7.5}\\\\ \to \bold{ x=\frac{7.5}{0.2}}\\\\ \to \bold{ x=37.5}\\\\$