Question

1. 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 20%. 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

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.

   => He spends:- (80/100)*500 = $400 on pizza

                                 & 500 -400 =$100 on gas

Now,

Assume price of Pizza = P_p & price of gas = P_G

Amount of pizza consumed = X_p & amount of gas consumed = X_G

Therefore , P_p X_p = 400

& P_GX_G = 100………………………………………….(i)

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.

                                                             {Since, new price = P_G + (40/100)P_G = (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 = (140/100)P_G* (80/100)X_G

                                                        = (112/100) P_GX_G = (112/100)*100……………..from (i)

                                                        =112

If he keeps spending all his money on pizza and gas,

=>    His current expenditure on Pizza = 500 -112

                                             =>P_pX¹_p = 388

Total percentage change in expenditure of pizza = (P_pX¹_p - P_p X_p)/ P_p X_p

                                                                                       = (X¹_p - X_p)/ X_p

{ Note, Given the price of pizza is fixed , all the change is in the amount of pizza consumed.}

   =>    The percentage change in his consumption of pizza (measured in slices)   is                                                      

                                                                                 = (X¹_p - X_p)/ X_p

                                                                                       =(P_pX¹_p - P_p X_p)/ P_p X_p

                                                                                = (388 – 400)*100/400

                                                                                = -3%

Therefore the consumption of pizza falls down by 3%.