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QuestionJoe's income grows by a constant amount each year. It was \$24,400 in year 1 and \$31,000 in year 7. When was it \$35,400?

Studdy Solution

STEP 1

Assumptions1. Joe's annual income increases each year by the same dollar amount. . The first year his income was 24,400.<br/>3.Theseventhyearhisincomewas24,400.<br />3. The seventh year his income was 31,000.
4. We need to find out in which year his income was $35,400.

STEP 2

First, we need to find out how much Joe's income increases each year. We can do this by subtracting the first year's income from the seventh year's income and then dividing by the number of years between the first year and the seventh year.
Annual increase=Income7th year−Income1st year7−1Annual\, increase = \frac{Income_{7th\, year} - Income_{1st\, year}}{7 -1}

STEP 3

Now, plug in the given values for the first year's income and the seventh year's income to calculate the annual increase.
Annual increase=$31,000−$24,4007−1Annual\, increase = \frac{\$31,000 - \$24,400}{7 -1}

STEP 4

Calculate the annual increase.
Annual increase=$31,000−$24,4007−1=$1,100Annual\, increase = \frac{\$31,000 - \$24,400}{7 -1} = \$1,100

STEP 5

Now that we have the annual increase, we can find out in which year Joe's income was 35,400.Wedothisbysubtractingthefirstyear′sincomefrom35,400. We do this by subtracting the first year's income from 35,400 and then dividing by the annual increase. We add1 to the result because the count starts from the first year.
Year=Incometarget−Income1st yearAnnual increase+1Year = \frac{Income_{target} - Income_{1st\, year}}{Annual\, increase} +1

STEP 6

Plug in the values for the target income, the first year's income, and the annual increase to calculate the year.
Year=$35,400−$24,400$1,100+1Year = \frac{\$35,400 - \$24,400}{\$1,100} +1

STEP 7

Calculate the year.
Year=$35,400−$24,400$1,100+1=11Year = \frac{\$35,400 - \$24,400}{\$1,100} +1 =11Joe's income was $35,400 in the11th year.

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