Math

QuestionRaul works 2h/day, Mon-Fri, and 8h on Sat at \$2 more/hour. He earns \$142/week. Find his weekday hourly rate.

Studdy Solution

STEP 1

Assumptions1. Raul works hours daily from Monday to Friday. . On Saturdays, he works8 hours.
3. His Saturday hourly wage is morethanhisweekdayhourlywage.<br/>4.Histotalweeklyearningsare more than his weekday hourly wage.<br />4. His total weekly earnings are 142.

STEP 2

Let's denote the weekday hourly wage as xx. Therefore, the Saturday hourly wage is x+2x +2.

STEP 3

Raul works2 hours per day for5 days (Monday to Friday), so he works a total of 2×5=102 \times5 =10 hours on weekdays.

STEP 4

Therefore, his earnings from the weekdays are 10x10x.

STEP 5

On Saturdays, he works8 hours at an hourly wage of x+2x +2, so his earnings on Saturday are 8(x+2)8(x +2).

STEP 6

His total weekly earnings are the sum of his weekday earnings and his Saturday earnings, which is 142.So,wecanwritetheequationas142. So, we can write the equation as10x+8(x+2)=14210x +8(x +2) =142$

STEP 7

Now, we need to solve this equation to find the value of xx.

STEP 8

First, distribute the8 in the term 8(x+2)8(x +2).
10x+8x+16=14210x +8x +16 =142

STEP 9

Combine like terms on the left side of the equation.
18x+16=14218x +16 =142

STEP 10

Subtract16 from both sides of the equation to isolate the term with xx.
18x=1421618x =142 -16

STEP 11

Calculate the right side of the equation.
18x=12618x =126

STEP 12

Divide both sides of the equation by18 to solve for xx.
x=12618x = \frac{126}{18}

STEP 13

Calculate the value of xx.
x=7x =7Raul makes $7 per hour on weekdays.

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