Question

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%. If he keeps spending all his money on pizza and gas, what is the percentage change in his consumption of pizza (measured in slices)?

Answer 1

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. $\frac{80}{100}\times 500=400$

He spends $400 on pizza

He spends 500-400=$100 on gas

Let the price of pizza be '$P_p$' and price of gas is '$P_g$'.

Let Amount of pizza consumed be $A_p$ and amount of gas be $A_g$

So, $P_p\times X_p=400$ ...(1)

$P_g\times X_g=100$  .....(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 = $\frac{140}{100}P_g$

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 = $\frac{140}{100}P_g\times \frac{80}{100}X_g$

Total amount now spent on gas = $\frac{112}{100}P_gX_g$

Total amount now spent on gas = $\frac{112}{100}\times 100$

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 $P_pX^1_p=338$

Total percentage change in expenditure of pizza is given by,

$C=\frac{(P_pX^1_p - P_p X_p)}{P_p X_p}\times 100$

$C=\frac{X^1_p- X_p}{X_p}\times 100$

$C=\frac{338-400}{400}\times 100$

$C=\frac{-62}{400}\times 100$

$C=-15.5\%$

Therefore the consumption of pizza falls down by 15.5%.