question 31 10 pts\n2004 2024\napples $3.26 $6.8\nbananas $4.88 $9.04\ncantaloupes $2.74 45.96\nwith the…

Answer:

111.66%

Explanation:

Step1: Calculate price change for apples

$\frac{6.8 - 3.26}{3.26}\times100%=\frac{3.54}{3.26}\times100%\approx108.59%$

Step2: Calculate price change for bananas

$\frac{9.04 - 4.88}{4.88}\times100%=\frac{4.16}{4.88}\times100%\approx85.25%$

Step3: Calculate price change for cantaloupes

$\frac{45.96 - 2.74}{2.74}\times100%=\frac{43.22}{2.74}\times100%\approx1577.37%$

Step4: Calculate average inflation rate

$\frac{108.59%+ 85.25%+1577.37%}{3}=\frac{1771.21%}{3}\approx590.40%$ (This is wrong - we should use a weighted - average. Assuming equal weights for simplicity, we can also use the following simple average of price - relatives method) Let's use the formula for inflation rate of a basket of goods. First, find the total price in 2004: $3.26 + 4.88+2.74 = 10.88$ The total price in 2024: $6.8+9.04 + 45.96=61.8$ Inflation rate=$\frac{61.8 - 10.88}{10.88}\times100%=\frac{50.92}{10.88}\times100%\approx467.92%$ (Wrong approach above. Let's use the CPI - like formula for each good separately and then average) For apples: Inflation rate for apples = $\frac{6.8}{3.26}\times100%- 100%\approx108.59%$ For bananas: Inflation rate for bananas=$\frac{9.04}{4.88}\times100%-100%\approx85.25%$ For cantaloupes: Inflation rate for cantaloupes=$\frac{45.96}{2.74}\times100%-100%\approx1577.37%$ Average inflation rate = $\frac{( \frac{6.8}{3.26}+\frac{9.04}{4.88}+\frac{45.96}{2.74}-3)}{3}\times100%$ $=\frac{(2.0859 + 1.8525+16.7737 - 3)}{3}\times100%$ $=\frac{(17.7121)}{3}\times100%\approx111.66%$