Answer: For the sum of 130
First: $90
Second: $40
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.
15a + 5 (130-a)=1550
15a+650-5a=1550
10a+650-650=1550-650
10a=900
a=$90 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
90+b=130
90-90+b=130-90
b= $40 was charged by the second mechanic
Step-by-step explanation:
After the movie, the family can spend 6 hours in Millersville.
36+4h=60
36+4h-36=60-36
4h=24
4h÷4=24÷4
h=6
So, after the move they can spend 6 hours there. (6×4=24, 24+36=60, they will spend $60 if they spend 6 hours there, $56 if they spend 5 hours there and don't want to spend $60).
$200 x 12 = 2,400 (number of pencils they bought in 2006)
3/4 x 2,400 = 1,800 (number of pencils they used)
2,400 - 1,800 = 600 (number of pencils remaining)
1,800 - 600 = 1,200 (number of pencils needed)
They had to buy 1,200 more pencils in 2007.
Solve for x. The multiplicity of a root is the number of times the root appears.
x=-7 (multiplicity of 1)
x=3 (multiplicity of 2)
x=2-i (multiplicity of 1)
x=2+1 (multiplicity of 1)