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1 answer:
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Answer:
The number of fast songs is 64 and the number of slow songs is 32
Step-by-step explanation:
∵ Y represents the number of fast songs
∵ x represents the number of slow dance songs
∵ John gets to play a total of 96 songs at his school dance
→ That means the sum of x and y is 96
∴ x + y = 96 ⇒ (1)
∵ He wants twice as many fast songs, y, as slow dance songs, x
→ That means y is twice x
∴ y = 2x ⇒ (2)
→ Substitute y in equation (1) by equation (2)
∵ x + 2x = 96
∴ 3x = 96
→ Divide both sides by 3 to find x
∴
∴ x = 32
→ Substitute the value of x in equation (2) to find the value of y
∵ y = 2(32)
∴ y = 64
∴ The number of fast songs is 64 and the number of slow songs is 32
Let's define:
So, you can set up a system of equations:
Now, to solve for both of those values, solve the system of equations:
Now, plug that y-value into the first equation to solve for x:
Now, we have both the values. The smaller value (x) = 11.57 and the bigger value (y) = 16.43.
So, you can set up a system of equations:
Now, to solve for both of those values, solve the system of equations:
Now, plug that y-value into the first equation to solve for x:
Now, we have both the values. The smaller value (x) = 11.57 and the bigger value (y) = 16.43.