Question

10. An accountant is calculating his client's monthly expenses. The following partially completed table provides the client's budget information as a percent of her take-home pay, and as both yearly and monthly dollar amounts. Help the accountant fill in the missing information in the table. (6 points: Part I - 3 points; Part II - 2 points; Part III - 1 point)Part I: What is the yearly dollar amount that the client spends on groceries? Use this yearly dollar amount to calculate the client's take-home pay.Part II: What percent of the client's take-home pay does she spend on housing? Use this percent and the client's take-home pay found in part I to calculate the yearly dollar amount and monthly dollar amount that the client spends on housing.Part III: Use the client's take-home pay found in part I to calculate the yearly dollar amount and monthly dollar amount that the client spends on other expenses.

Answer 1

Hello there. To solve this question, we'll have to remember some properties about yearly and monthly expenses and fill the table.

Given the partially filled table with informations about the client's expenses:

First, we notice that if he expends $400 with groceries monthly, we can multiply this amount by 12 to find the yearly amount:

$400 * 12 = $4800

If $400 represents 10% of what he can expend with groceries monthly, we can set the following ratio to find how much he expends with other things:

$\frac{400}{0.1}=\frac{other}{0.47}$

Multiply both sides of the equation by 0.47 and calculate the fraction

$\text{other}=\frac{400\cdot0.47}{0.1}=1880$

And again, by multiplying it by 12, we find the yearly dollar amount for other expenses:

$1880\cdot12=22560$

Now, to fill the first column, knowing the percent with groceries and other expenses add up to 57%, this means that the percent for housing must be 43%.

Again, by setting a ratio, we can find how much money will he expend monthly on housing comparing to the other informations:

$\frac{monthly}{0.43}=\frac{400}{0.1}$

Multiply both sides of the equation by a factor 0.43 and calculate the fraction

$\text{monthly}=1720$

Finally, multiply this number by 12 to find the yearly dollar amount:

$1720\cdot12=20640$

With those informations, we can answer the questions for Part I, II and III:

I. What is the yearly dollar amount that the client spends on groceries: $4800.

II. What percent of the client's take-home pay does she spend on housing? 43%.

III. Use the client's take-home pay in part I to calculate the yearly and monthly dollar amount that the client spends on other expenses: $22560 and $1880, respectively.