Paul has a sum of $260 in $5 and $10 bills. If he has 40 bills in total, how many were of each denomination?

28 5 dollar bills

12 10 dollar bills

Step-by-step explanation:

You can write two equations to model this situation'

x will be the number of 5 dollar bills

y will be the number of 10 dollar bills

x+y=40

5x+10y=260

There are a couple of ways you can solve this but but I will be doing it through substitution because that looks easier (I can explain other methods if you're interested)

So we have x+y=40

If I subtract y from both sides and divide by -1 we get

-x+40=y

We can then plug this value in for y in the second equation

5x+10(-x+40)=260

Distribute the 10 and combine like terms to get

-5x+400=260

subtract 400 from both sides and divide by -5 to get

x=28

This means that there are 28 5 dollar bills. We can plug this value back in for x into our first equation to solve for y

28+y=40

Subtract 28 from both sides

y=12

This means that there were a total of 28 5 dollar bills and 12 10s

I doubled checked this in desmos and it checks out

4+4+2x

or

2x+8

step-by-step explanation:

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20