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lunaandrew332
31.01.2021 •
Mathematics
The owner of a grocery store wants to mix two types of candy together to make 15 lbs that he he can sell for $5.00 per lb. He wants to use chocolate candy's that he sells for $7:00 a pound and sugar candies that he sells for 2.00 per pound. How many pounds of each should the owner use.
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Ответ:
9 pounds of chocolate and 6 pounds of sugar candies
Step-by-step explanation:
Let's define the variables:
C = pounds of chocolate candies used.
S = pounds of sugar candies used.
We know that he wants to make a total of 15lb, then:
C + S = 15
We also want that the price per pound to be equal to 5$.
This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.
C*$7.00 + $2.00*S = $5.00*15
Then we have a system of equations:
C + S = 15
C*$7.00 + $2.00*S = $5.00*15
To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:
C = 15 - S
now we can replace that in the other equation:
(15 - S)*$7.00 + $2.00*S = $5.00*15
Now we can solve this for S.
$105 - $5.00*S = $75
$105 - $75 = $5.00*S
$30 = $5.00*S
$30/$5 = S = 6
Then there are 6 pounds of sugar candy, and we can use the equation:
C + S = 15
C + 6 = 15
C = 15 - 6 = 9
There are 9 pounds of chocolate candy in the mix.
Ответ:
9 pounds of chocolate candies, 6 pounds of sugar candies.
Step-by-step explanation:
We can set the amount of chocolate candies to x and the amount of sugar candies to 15 - x.
Our equation is:
7x + 2(15 - x) = 5 * 15.
Simplified:
7x + 30 - 2x = 75.
x = 9.
9 pounds of chocolate candies.
15 - 9 = 6.
6 pounds of sugar candies.
Ответ: