Question

1. One of two numbers is two thirds the other number. The sum of the numbers is 45. Find the numbers

2. One of two numbers is five more than the other. The sum of the numbers is 17. Find the numbers.

3. The first number is 8 more than the second number. Theee times the second number plus twice the first number is equal to 26. Find the numbers.

4. Dan has five times as many 1$ bills as 5$ bills. He has a total of 48 bills. How many of each does he have?


Please please please help and show work this is due tomorrow and I’m so confused! Thank you

Answer 1

1. You can set up 2 equations like so:

`y = (2)/(3) * x \\ x + y = 45`
You can then subsitute the y in the second equation with the first one.

`(2)/(3)x + x = 45 \\ (2)/(3)x + (3)/(3) x = 45 \\ (5)/(3) x = 45`
And then you can multiply both sides by the reciprocal of 5/3.

`x = 45 * (3)/(5) \\ x = (135)/(5) \\ x = 27`
Then you can put this x into one of the equations to get the y like so:

`y = (2)/(3) * 27 \\ y = (54)/(3) \\ y = 18`
So your two numbers would be 18 and 27.


2. This is going to be similar to the first problem so I will cut down on the descriptions and just show the work.

`y = 5 + x \\ y + x = 17`
Subsitute again.

`x+ x + 5= 17 \\ 2x + 5 =17 \\`
Subtract 5.

`2x = 12 \\ x = 6`
Plug 6 back into one of the equations.

`y = 6 + 5 \\ y = 11`
Your two numbers are 11 and 6.
3. This is a bit more complicated but the same logic applies here.

`y = 8 + x \\ 3x + 2y = 26`
Subsitute again and solve for x.

`3x + 2(x + 8) = 26 \\ 3x + 2x + 16 = 26 \\ 5x + 16 = 26 \\ 5x =10 \\ x = 2`
Then plug it in again.

`y = 8 + 2 \\ y = 10`
Your two numbers are 2 and 10.

4. For this one, I'm going to have the $1 bills as y and the $5 bills as x.


`y = 5x \\ x + y = 48`
Subsitute and solve for x.

`x + 5x = 48 \\ 6x = 48 \\ x = 8`
Plug x back into an equation.

`y = 5 * 8 \\ y = 40`
Thus, Dan has 40 $1 bills and 8 $5 bills. I hope this helps.