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QuestionBen works 4 hours daily and earns the same total as Allen. What is Ben's hourly wage?
Set up: 8(10)=4(x)8(10)=4(x) Identify: Ben's wage is the unknown. Strategize: Let x=x= Ben's unknown wages. Solve: x=20x=20 Check: 8(10)=4(20)8(10)=4(20)

Studdy Solution

STEP 1

Assumptions1. Allen works8 hours each day. Allen earns $10 per hour3. Ben works4 hours each day4. Ben earns the same total amount per day as Allen5. We need to find Ben's hourly wage, which is the unknown

STEP 2

First, we need to calculate how much Allen earns per day. We can do this by multiplying the number of hours Allen works by his hourly wage.
Allen′s daily earnings=Hours worked by Allen per daytimesAllen′s hourly wageAllen's\, daily\, earnings = Hours\, worked\, by\, Allen\, per\, day \\times Allen's\, hourly\, wage

STEP 3

Now, plug in the given values for the number of hours Allen works and his hourly wage to calculate his daily earnings.
Allen′s daily earnings=8 hourstimes$10 per hourAllen's\, daily\, earnings =8\, hours \\times \$10\, per\, hour

STEP 4

Calculate Allen's daily earnings.
Allen′s daily earnings=8 hourstimes$10 per hour=$80Allen's\, daily\, earnings =8\, hours \\times \$10\, per\, hour = \$80

STEP 5

Now that we know Allen's daily earnings, we can set up an equation to find Ben's hourly wage. We know that Ben's total daily earnings are the same as Allen's, so we can set up the equation as followsHours worked by Ben per daytimesBen′s hourly wage=Allen′s daily earningsHours\, worked\, by\, Ben\, per\, day \\times Ben's\, hourly\, wage = Allen's\, daily\, earnings

STEP 6

Substitute the known values into the equation.
4 hourstimesx=$804\, hours \\times x = \$80Here, xx represents Ben's unknown hourly wage.

STEP 7

To solve for xx, we need to isolate xx on one side of the equation. We can do this by dividing both sides of the equation by the number of hours Ben works each day.
x=$80/4 hoursx = \$80 /4\, hours

STEP 8

Calculate the value of xx.
x=$80/4 hours=$20 per hourx = \$80 /4\, hours = \$20\, per\, hourSo, Ben earns $20 per hour.

STEP 9

Finally, we should check our solution. We can do this by substituting the value of xx back into the original equation and making sure both sides of the equation are equal.
8 hourstimes$ per hour=4 hourstimes$20 per hour8\, hours \\times \$\, per\, hour =4\, hours \\times \$20\, per\, hourBoth sides of the equation equal 80,sooursolutioniscorrect.Benearns80, so our solution is correct. Ben earns 20 per hour.

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