Could you please help me with this?
Music Spending. Sean has $37 to spend. He can spend all of it on two compact discs and a casette, or he can buy one CD and two cassettes and have $5.00 left over. What is the price of a CD? of a casette?
Since he has no money left after buying two CDs, then each CD is $18.50.
If he buys one CD (for $18.50) and one cassette, and has $5 left over, he must have spent ___ on the cassette.
You don't need algenra to to this.
Certainly! Let's break down the problem to find the price of a CD and a cassette.
Let's assume the price of a CD is represented by "x" dollars and the price of a cassette is represented by "y" dollars.
According to the given information, Sean has $37 to spend. So, we can write the first equation as:
2x + y = 37 ... (Equation 1)
It is also mentioned that if Sean buys one CD and two cassettes, he will have $5.00 left over. Using this information, we can write another equation as:
x + 2y = 37 - 5 ... (Equation 2)
Simplifying Equation 2, we get:
x + 2y = 32 ... (Equation 3)
Now we have a system of equations:
Equation 1: 2x + y = 37
Equation 3: x + 2y = 32
To solve this system, we can use the method of substitution or elimination. In this case, let's use the method of elimination.
If we multiply Equation 3 by 2, we get:
2(x + 2y) = 2(32)
2x + 4y = 64 ... (Equation 4)
Now, we can subtract Equation 1 from Equation 4:
(2x + 4y) - (2x + y) = 64 - 37
2x + 4y - 2x - y = 27
3y = 27
y = 9
Now that we know the price of a cassette is $9, we can substitute this value back into either Equation 1 or Equation 3 to find the price of a CD.
Using Equation 1:
2x + (9) = 37
2x + 9 = 37
2x = 37 - 9
2x = 28
x = 14
Therefore, the price of a CD is $14, and the price of a cassette is $9.
Hope this explanation helps you understand how to solve this kind of problem!