Algebra equation

Question

Hailey went to the bank to withdraw $440. She received 30 bills altogether.

There were some fives, some tens, and some twenty-dollar bills. Hailey

received four times as many twenty-dollar bills as five-dollar bills. How many

ten-dollar bills did Hailey receive?

Answer 1

Here's another approach: x = no. of 5's; y = no. of 10's; z = no. of 20's

For the number of bills: x + y + z = 30, but we know that z = 4x, so x + y + 4x -> 5x + y = 30

For the value: 5x + 10y + 20z = 440, again substituting 5x + 10y + 20(4x) = 440 ->85x + 10y = 440

So we have simultaneous equations; 5x + y = 30 and 85x + 10y = 440

Since they're asking for y, can eliminate the x terms if mult 1st eqn by -17

-85x - 17y = -510

85 x + 10y = 440

-7y = -70 and y = 10 $10 bills.

You can figure out the other two denominations to check that they add to 30 bills and $440.

Answer 2

x+y+z = 30

z=4x

5x +y = 30

85x +17y = 510

5x+10y+20z = 440

5x +10y +20(4x) = 440

85x +10y = 440

7y = 70

y=10 = 10 Ten dollar bills

5x =30-10=20

x =20/5 =4 Five dollar bills

z=4x = 16 Twenty dollar bills

x+y+z= 4+10+16 = 30