Respuesta :
Answer:
The consumption of pizza falls down by 15.5%.
Step-by-step explanation:
Given : Stephanos spends all of his $500 allowance on slices of pizza and gas for his pickup truck. He spends eighty percent of this on pizza and the rest on gas. Because of a shortage of gas, the price of gas increases by 40%. This makes his consumption of gas (measured in gallons) fall by 40%.
To find : What is the percentage change in his consumption of pizza ?
Solution :
He spends eighty percent of this on pizza and the rest on gas.
i.e. [tex]\frac{80}{100}\times 500=400[/tex]
He spends $400 on pizza
He spends 500-400=$100 on gas
Let the price of pizza be '[tex]P_p[/tex]' and price of gas is '[tex]P_g[/tex]'.
Let Amount of pizza consumed be [tex]A_p[/tex] and amount of gas be [tex]A_g[/tex]
So, [tex]P_p\times X_p=400[/tex] ...(1)
[tex]P_g\times X_g=100[/tex] .....(2)
Because of a shortage of gas, the price of gas increases by 40%.
The price of gas is now 140% of what it was earlier.
New price = [tex]\frac{140}{100}P_g[/tex]
Price increase makes his consumption of gas (measured in gallons) fall by 20%.
He is consuming 80% of the gas now as compared to the previous amount
Total amount now spent on gas = [tex]\frac{140}{100}P_g\times \frac{80}{100}X_g[/tex]
Total amount now spent on gas = [tex]\frac{112}{100}P_gX_g[/tex]
Total amount now spent on gas = [tex]\frac{112}{100}\times 100[/tex]
Total amount now spent on gas = Rs.112
If he keeps spending all his money on pizza and gas,
His current expenditure on Pizza = Rs. 500 -112 =Rs.388
Let [tex]P_pX^1_p=338[/tex]
Total percentage change in expenditure of pizza is given by,
[tex]C=\frac{(P_pX^1_p - P_p X_p)}{P_p X_p}\times 100[/tex]
[tex]C=\frac{X^1_p- X_p}{X_p}\times 100[/tex]
[tex]C=\frac{338-400}{400}\times 100[/tex]
[tex]C=\frac{-62}{400}\times 100[/tex]
[tex]C=-15.5\%[/tex]
Therefore the consumption of pizza falls down by 15.5%.
