# I need a formula to this problem: solve x = 20000, y = 15% of z, y + z = x for y, z

#### Mort

##### New member
Hi, this is my first post. I need a formula to the following problem:

x = 20000
y = 15% of z
y + z = x

How do you solve for y and z? What is the formula to the solution?

With x being 20000 I know that roughly y = 2608.7 and z = 17391.3, but that was just from me guessing and then adjusting a few dozen times. I need to know the actual formula to solve for y and z.

And this has a practical purpose if anyone is interested. We own a small business and we have a certain budget for marketing. That budget needs to include commission to the marketing company and what is left will go to the actual ad spend. The commission is 15% of the ad budget. So as our budget goes up or down I need to be able to calculate what the commission and ad spend will be without going over our overall budget. I can continue to guess and adjust but there must be a more practical formula to do that.

Thanks,

-Mort

#### Harry_the_cat

##### Senior Member
Hi, this is my first post. I need a formula to the following problem:

x = 20000
y = 15% of z
y + z = x

How do you solve for y and z? What is the formula to the solution?

With x being 20000 I know that roughly y = 2608.7 and z = 17391.3, but that was just from me guessing and then adjusting a few dozen times. I need to know the actual formula to solve for y and z.

And this has a practical purpose if anyone is interested. We own a small business and we have a certain budget for marketing. That budget needs to include commission to the marketing company and what is left will go to the actual ad spend. The commission is 15% of the ad budget. So as our budget goes up or down I need to be able to calculate what the commission and ad spend will be without going over our overall budget. I can continue to guess and adjust but there must be a more practical formula to do that.

Thanks,

-Mort
Since x=20000 and y + z = x, then y + z = 20000.
Since y = 15% of z, then y = 0.15z

Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

Dividing both sides by 1.15 gives z = 17391.30

Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

Hope that helps.

#### jtayag0622

##### New member
Since x=20000 and y + z = x, then y + z = 20000.
Since y = 15% of z, then y = 0.15z

Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

Dividing both sides by 1.15 gives z = 17391.30

Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

Hope that helps.
This is absolutely right.

#### Mort

##### New member
Since x=20000 and y + z = x, then y + z = 20000.
Since y = 15% of z, then y = 0.15z

Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

Dividing both sides by 1.15 gives z = 17391.30

Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

Hope that helps.
Thank you so much! My brain was really hurting when I was trying to figure this out. I'll be plugging this into an excel sheet to help us make the calculations. Thanks again!