High School

Ryan is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $7.40 per hour. How many hours did he work at each job the week that he made $150.80?

Answer :

Answer:

Step-by-step explanation:

a+b = 22 -- equation 1

6.20a + 7.40b = 150.80 replacing decimals

620a + 740b = 15080 --- equation 2

From eq. 1 a = (22 - b)

putting a's value in equation 2

620(22 - b) + 740b = 15080

13640 - 620b + 740b = 15080

120b = 15080 - 13640

b = 1440/120 = 12

From equation 1 a + 12 = 22

a = 10

Verify your answer by equation 2 putting the value of a and b

620*10 + 740*12 = 15080

We could write the following equations according to the problem:

Hours equation:

[tex]a+b=22[/tex]

And, the payment equation: (cents)

[tex]620a+740b=1508[/tex]

We could solve this system of equations using the elimination method:

[tex]\begin{cases}a+b=22 \\ 620a+740b=1508\end{cases}[/tex]

We're going to multiply the first equation by -620:

[tex]\begin{cases}-620a-620b=-13640 \\ 620a+740b=15080\end{cases}[/tex]

Now, we're going to sum both equations eliminating variable a, so we get a linear equation in terms of b:

[tex]\begin{gathered} 120b=1440 \\ b=12 \end{gathered}[/tex]

Now we know that he did 12 hours at job b.

As he worked 22 hours in total, then he worked 10 hours at job a.

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