Question

Ms ann wants to make candy mix that costs $2.00 per pound. if she has already selected 80 pounds that costs $2.40 per pound for the mix. How much candy that costs $1.80 per pound can she use

Answer 1

Ms. Ann can use 160 pounds of candy that costs $1.80 per pound to maintain an average cost of $2.00 per pound for the candy mix.

How to find How much candy that costs $1.80 per pound can she use

Let's assume Ms. Ann wants to use x pounds of candy that costs $1.80 per pound.

The total cost of the candy mix can be calculated as follows:

Total cost = Cost of selected candy + Cost of additional candy

The cost of selected candy is given as 80 pounds at $2.40 per pound:

Cost of selected candy = 80 pounds * $2.40/pound = $192.00

The cost of additional candy is x pounds at $1.80 per pound:

Cost of additional candy = x pounds * $1.80/pound = $1.80x

Since the total cost should be $2.00 per pound for the candy mix, we can write the equation:

Total cost = Cost of selected candy + Cost of additional candy = $2.00 per pound * (80 pounds + x pounds)

Substituting the values:

$192.00 + $1.80x = $2.00 * (80 + x)

Simplifying the equation:

$192.00 + $1.80x = $160.00 + $2.00x

Rearranging the terms:

$0.20x = $32.00

Dividing both sides by $0.20:

x = $32.00 / $0.20

x = 160 pounds

Therefore, Ms. Ann can use 160 pounds of candy that costs $1.80 per pound to maintain an average cost of $2.00 per pound for the candy mix.

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Answer 2

Answer:

  $160 pounds

Step-by-step explanation:

You want to know how much candy that costs $1.80 per pound to add to 80 pounds of candy costing $2.40 per pound to make a mix that costs $2.00 per pound.

Proportion

The proportion of the components in the mix is the reverse of the proportion of the differences between the component value and the mix value. The attached diagram shows this.

The difference between the high-value component value ($2.40 per pound) and the mix value ($2.00 per pound) is $0.40 per pound. Likewise the difference between the mix value and the low-value component is $2.00 -1.80) = $0.20 per pound. Then the ratio of high-value component to low-value component will be 0.20 : 0.40 = 1 : 2.

Solution

If there are 80 pounds of expensive candy, there needs to be 2×80 = 160 pounds of cheap candy in the mix to makes its value $2.00 per pound.

Ms. Ann should use 160 lb of candy costing $1.80 per pound.

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Additional comment

This sort of X-diagram can be used for mixtures of all sorts. Some checks you can used are ...

• the sum of "ratio units" is the difference in value of the components, 0.20 +0.40 = 0.60 = 2.40 -1.80 (Some problems require you work backwards from this total. Here, for example, the low-value component is 0.40/0.60 = 2/3 of the total mix weight.)
• the proportion of lower-value component will be greater if the mix has a value less than the average of the two component values. Here, the average of $2.40 and 1.80 is $2.10. Since the mix has a lower value, at $2.00, there will be more of the $1.80 candy in the mix than of the $2.40 candy.

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