Question

the bar graph shows the average annual spending per person on selected items in 2010. the combined spending on housing, vehicles/gas, and health care was $13,911. the difference between spending on housing and spending on vehicles/gas was $3761. the difference between spending on housing and spending on health care was $535. find the average per - person spending on housing, vehicles/gas, and health care in 2010. find the average per - person spending on housing in 2010.

Explanation:

Step1: Define Variables

Let \( H \) = housing spending, \( V \) = vehicles/gas spending, \( HC \) = health care spending.
Given:

• \( H + V + HC = 13911 \) (combined spending)
• \( H - V = 3761 \) (housing - vehicles/gas difference)
• \( HC - H = 535 \) (health care - housing difference)

Step2: Express \( V \) and \( HC \) in Terms of \( H \)

From \( H - V = 3761 \), we get \( V = H - 3761 \).
From \( HC - H = 535 \), we get \( HC = H + 535 \).

Step3: Substitute into Combined Spending Equation

Substitute \( V \) and \( HC \) into \( H + V + HC = 13911 \):
\( H + (H - 3761) + (H + 535) = 13911 \)

Step4: Simplify and Solve for \( H \)

Simplify the left - hand side:
\( H + H - 3761 + H + 535=3H - 3226 \)
Set equal to 13911:
\( 3H - 3226 = 13911 \)
Add 3226 to both sides:
\( 3H=13911 + 3226=17137 \)
Divide by 3:
\( H=\frac{17137}{3}\approx5712.33 \) (Wait, let's check the arithmetic again. Wait, 13911+3226: 13911 + 3000 = 16911, 16911+226 = 17137. Then \( H=\frac{17137}{3}\approx5712.33 \)? Wait, maybe I made a mistake in setting up the equations. Wait, the problem says "The combined spending on housing, vehicles/gas, and health care was $13,911. The difference between spending on housing and spending on vehicles/gas was $3761. The difference between spending on housing and spending on health care was $535. Find the average per - person spending on housing, vehicles/gas, and health care in 2010." Wait, no, the sub - question is "Find the average per - person spending on housing in 2010."

Wait, let's re - examine the problem. Let's define:

Let \( H \) = housing spending, \( V \) = vehicles/gas spending, \( HC \) = health care spending.

We know that:

1. \( H+V + HC=13911 \)

1. \( H - V = 3761\Rightarrow V=H - 3761 \)

1. \( HC - H=535\Rightarrow HC = H + 535 \)

Now substitute \( V \) and \( HC \) into the first equation:

\( H+(H - 3761)+(H + 535)=13911 \)

Combine like terms:

\( H+H+H-3761 + 535=13911 \)

\( 3H-(3761 - 535)=13911 \)

\( 3H - 3226=13911 \)

\( 3H=13911 + 3226=17137 \)

\( H=\frac{17137}{3}\approx5712.33 \)? Wait, that seems odd. Wait, maybe the difference between health care and housing is \( H - HC = 535 \) (maybe I misread the difference direction). Let's assume the other way: if the difference between spending on housing and health care is $535, so \( H - HC=535\Rightarrow HC = H - 535 \)

Then substitute into the first equation:

\( H+(H - 3761)+(H - 535)=13911 \)

Combine like terms:

\( 3H-(3761 + 535)=13911 \)

\( 3H - 4296=13911 \)

\( 3H=13911 + 4296=18207 \)

\( H=\frac{18207}{3}=6069 \)

Ah, that makes more sense. So probably the difference is \( H - HC = 535 \) (housing - health care = 535), so \( HC = H - 535 \)

Let's re - do the steps:

Step2 (corrected): Express \( V \) and \( HC \) in Terms of \( H \)

From \( H - V = 3761 \), \( V = H - 3761 \)

From \( H - HC = 535 \), \( HC = H - 535 \)

Step3 (corrected): Substitute into Combined Spending Equation

\( H+(H - 3761)+(H - 535)=13911 \)

Step4 (corrected): Simplify and Solve for \( H \)

Combine like terms: \( 3H-(3761 + 535)=13911 \)

\( 3H - 4296 = 13911 \)

Add 4296 to both sides: \( 3H=13911 + 4296 = 18207 \)

Divide by 3: \( H=\frac{18207}{3}=6069 \)

Answer:

The average per - person spending on housing in 2010 is \(\$6069\)