Question

A candy store owner wants to mix some candy costing $1.25 a pound

Answer 1

• 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.

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

• It implies that $\bold{37.5\ pounds}$ of candy at $\bold{\ 1.25}$ a pound must be used to make the final concoction.

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Answer 2

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 pound
• The resulting mixture should be 50 pounds of candy
• The 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.

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