Problem 7.2. Petya bought himself shorts for football at the store.

- If he had bought shorts with a T-shirt, the cost of the purchase would have been twice as much.
- If he had bought shorts with cleats, the cost of the purchase would have been five times as much.
- If he had bought shorts with shin guards, the cost of the purchase would have been three times as much.

How many times greater would the cost of the purchase have been if Petya had bought shorts, a T-shirt, cleats, and shin guards?
Answer: 8.

Solution. Let the shorts cost $x$. Since the shorts with a T-shirt cost $2x$, the T-shirt also costs $x$. Since the shorts with boots cost $5x$, the boots cost $4x$. Since the shorts with shin guards cost $3x$, the shin guards cost $2x$. Then, if Petya bought shorts, a T-shirt, boots, and shin guards, his purchase would amount to $x+x+4x+2x=8x$, which is 8 times more than $x$.