Question

Lin is paid $90 for 5 hours of work. She used the following table to calculate how much she would be paid at this rate for 8 Hours of work. 1. What is the meaning of the 18 that appears in the table? 2. Explain how Lin used this table to solve the problem. 3. At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work. AMOUNTS EARNED ($) | TIME WORKED(hours)

Answer 1

Let

y ------> the amount earned

x ----> the number of hours worked

In this problem we have a direct variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality

k=y/x

In this problem the value of k is hourly rate

so

we have

For y=$90 -------> x=5 hours

substitute

k=90/5

k=$18 per hour

substitute in the linear equation

y=18x

so

Part 1) What is the meaning of the 18 that appears in the table?

18 is the hourly rate ( amount earned by a one hour of work)

Part 2) Explain how Lin used this table to solve the problem.

using the table

For x=8 hours

the value of y=$144

Verify with the equation

y=18x

y=18(8)=144 -----> is ok

Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.

For x=3 hours

substitute in the equation

y=18x

substitute the value of x

y=18(3)=$54

For x=2.1 hours

y=18(2.1)=$37.8