10 points if u can answer these few word problems...?

Question

Show work on all please i want to learn... 2

Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?

Taylin has eighty-one coins in her purse. She only carries dimes and nickels. The value of her collection is $5.70. How many dimes does she have?

Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.

Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many quarters and nickels do you have?

There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many adult and student tickets were sold?

An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air.

Please show work so I can understand!!!

Answer 1

i'll do the first so you can learn

let the cost (in dollars) of an apple be a and the cost of a pear be p, then we have two equations:

6p+3a=3.90

2p+5a=3.30

leave the first equation as is, and multiply the second by 3 to get

6p+3a=3.90

6p+15a=9.90

subtract the first from the second

12a=6

a=0.5

now insert the value of a in the first equation

6p+3*0.5=3.90

6p=2.40

p=0.40

so one pear costs 40 cent