David keeps records of his monthly earnings. Last month he worked 120 hours and earned $2700. This month he worked 100 hours and earned $2300. Which equation could you use to find \( f(x) \), the amount he would earn at this rate if he worked \( x \) hours?

A. \( f(x) = 120x + 400 \)

B. \( f(x) = 400x \)

C. \( f(x) = 100x + 300 \)

D. \( f(x) = 20x + 300 \)

substitute x in the equations for numbers of hours worked, and you should look for the one that gets the right amount of money.
If you use 120 hours, you should look for the equation that gives you the answer of 2700:
f(x)=120x+400 120(120) + 400 =14800
f(x)=400x 400(120) = 48000
f(x)=100x+300 100(120) + 300 =12300
f(x)=20x+300 **20(120) + 300 = 2700 **
Just to check, use the other number of hours: 100 hours.. You should expect to see an answer of 2300: ****f(x)=20x+300 ****20(100) + 300 = **2300 **
the equation you want is f(x)=20x+300

Answered by jsef | 2024-06-10

f(x) = 20x+300 you sub in the x values (120 hours and 100 hours) for each equation the only one they both work for is the last one f(x) = 20x + 300 f(100) = (20 * 100) + 300 = 2000 + 300 = 2300
f(120) = (20 * 120) + 300 = 2400 + 300 = 2700

Answered by 09brinee | 2024-06-10

David's earnings function can be represented by the equation f ( x ) = 20 x + 300 . This correctly calculates his earnings for both the 120 hours worked last month and the 100 hours worked this month. Thus, the correct option is D.
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Answered by jsef | 2024-10-15