Question

1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?

2) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $305.00. Find the number of twenty-dollar bills. What is the equation?

Answer 1

Part 1) Helen's age is 32 years old and Jane's age is 24 years old

Part 2) 13 twenty-dollar bills

Explanation:

Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?

Let

x----> Helen's age

y---> Jane's age

we know that

x=y+8 ----> equation A

(x-20)=3(y-20) -----> equation B

substitute equation A in equation B and solve for y

(y+8-20)=3(y-20)

y-12=3y-60

3y-y=60-12

2y=48

y=24 years

Find the value of x

x=y+8

x=24+8=32 years

Part 2)

Let

x-----> the number of five-dollar bills

y----> the number of twenty-dollar bills

we know that

5x+20y=305 -----> equation A

y=x+4 ------> x=y-4 ------> equation B

substitute equation B in equation A and solve for y

5(y-4)+20y=305

5y-20+20y=305

25y=325

y=13 twenty-dollar bills

Find the value of x

x=y-4

x=13-4=9 five-dollar bills