A store is selling compact discs for $10.50 and $8.50. You buy 10 discs and spend a total of $93. How many compact discs did you buy for $10.50? $8.50?
What's the equation?
6 used cds
4 new cds
To find out how many compact discs you bought for $10.50 and $8.50, let's set up a system of equations.
Let's represent the number of compact discs you bought for $10.50 as "x" and the number of compact discs you bought for $8.50 as "y".
According to the given information, you bought a total of 10 compact discs, so we can write the first equation as:
x + y = 10 ...equation 1
The total amount you spent on the compact discs is $93, so we can write the second equation as:
10.50x + 8.50y = 93 ...equation 2
Now, we can solve this system of equations to find the values of x and y.
Multiplying the first equation by 8.50 and the second equation by 1.50 to eliminate the y variable, we get:
8.50x + 8.50y = 85 ...equation 3
15.75x + 12.75y = 139.5 ...equation 4
Subtracting equation 3 from equation 4:
(15.75x + 12.75y) - (8.50x + 8.50y) = 139.5 - 85
7.25x + 4.25y = 54.5 ...equation 5
Now, we have two equations:
7.25x + 4.25y = 54.5 ...equation 5
10.50x + 8.50y = 93 ...equation 2
We can solve this system of equations using substitution or elimination method.
Let's use the elimination method to solve this system of equations:
Multiplying equation 5 by 2 to eliminate the x variable, we get:
14.50x + 8.50y = 109 ...equation 6
Subtracting equation 2 from equation 6:
(14.50x + 8.50y) - (10.50x + 8.50y) = 109 - 93
4x = 16
x = 4
Now, substitute the value of x back into equation 1 to find the value of y:
4 + y = 10
y = 10 - 4
y = 6
Therefore, you bought 4 compact discs for $10.50 and 6 compact discs for $8.50.