10-04-2007
A hair salon receives a shipment of 84 bottles of hair conditioner to use and sell to customers. The two types of conditioners received are type A, which is used for regular hair, and type B, which is used for dry hair. Type A costs $6.50 per bottle and type B costs $8.25 per bottle. The hair salon's invoice for the conditioner is $588. How many of each type of conditioner are in the shipment?
Type A = x Type A = $6.50 then x = $6.50
Type B = y Type B = $8.25 then y = $8.25
Total Types = 84
Total Invoice = $588
So, you now have two separate equations with two variables in each one.
We know that the total amount of bottles received was 84. Following that:
X + Y = 84
We know that the total amount spent on the conditioners was $588. Because Type A is $6.50 and we have labeled Type A as variable x, we get:
6.50x + 8.25y = 588
Since you have two variables you need to set up one equation equaling one of the variables. Since X + Y = 84 is the easiest, we will start with that.
X + Y = 84
X = 84 – Y
Then plug it into the other equation.
6.50(84 – Y) + 8.25Y = 588
546 – 6.50Y + 8.25Y = 588
546 + 1.75Y = 588
1.75Y = 42
Y = 24
So, 24 bottles of Type B shampoo were sold. Then plug that number into the easiest equation.
X + Y = 84
X + 24 = 84
X = 60 |