Question

candy that costs 31 cents per pound is mixed with candy that costs 46 cents per pound to obtain 50 pounds of candy that costs 40 cents per pound. How many pounds of each of the two types of candy are in the mix?

Answer 1

Answer:

20 lb of 31 cent candy, 30 lb of 46 cent candy

Step-by-step explanation:

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Answer 2

The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we can assume the separate weights of each type of candies to be represented by variables.

Let we have:

• x = weight (in pounds) of first type of candy whose cost is 31 cents per pound.
• y = weight (in pounds)  of second type of candy whose cost is 46 cents per pound.

x pounds of first type of candy is mixed with y pounds of second candy.

The weight of the mixture = x + y = 50 pounds

The cost of the mixture = 40 cents per pound  = $40 \times 50 = 2000$ cents

Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = $31x + 46y$
Thus, we get $31x + 46y =2000$

Therefore, we got a system of two linear equations as:

$x +y = 50\\31x + 46y =2000$

From first equation, we get:

$x = 50 -y$

Substituting this value in second equation, we get:

$31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30$

Putting this value of y in equation for x, we get:

$x = 50-y = 50-30 = 20$

Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

Learn more about solving system of linear equations here:

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