How Do You Solve a Word Problem Involving Charitable Donations?

[NotaMathPerson]

Hello! Please take a look at so,ution to the problem

X, Y, and Z donated a sum of \$525 to a charity. For every dollar that X gives, Y gives 25 cents, and Z 50 cents. How much did each donate?

My solution

Let $x=$ amount donated by X
$25x=$ amount donated by y
$50x=$ amount donated by z

$x+\frac{50x}{100}+\frac{25x}{100}=525$

Solving for $x$ I get $x=$ \$300

Therefore $x=\$300$
$y=\$75$
$z=\$150$

Second method(thiss is where I am having trouble)

Let $x=$ amount donated by X
$25x=$ amount donated by y
$50x=$ amount donated by z

I convert everything into cents
$100x+50\cdot x\cdot100+25x\cdot100=52500$

Solving for x I get a different answer.

My thought process was the variable $x$ is in dollars hence I multiplied every term and both sides of the equation by 100 to convert it to cents.
Please tell me where I was wrong. Thanks!

 

[Greg]

With everything converted to cents the correct equation would be 100x + 50x + 25x = 52500.
You can see this by multiplying both sides of the equation you wrote for your first solution by 100.

 

[NotaMathPerson]

With everything converted to cents the correct equation would be 100x + 50x + 25x = 52500.
You can see this by multiplying both sides of the equation you wrote for your first solution by 100.

Hello! Does that mean that whatever value of x I get in my 2nd solution is also in cents and be divided by 100 to convert back to dollar?

 

[Greg]

No. x is in dollars. Do you see why?

 

[NotaMathPerson]

No. x is in dollars. Do you see why?

Hello again!

that is what confusing me. If x in my 2nd solution is in dollars, it should be multiplied by 100 to convert it to cents, juts the way i divided 50x by hundred to convert it to dollars. Please bear with me.

 

[Greg]

Say I have x dollars. To convert to cents I multiply by 100. That gives me 100x cents.

For every dollar person "x" gives, person "z" gives half of that, or 50x cents and person "y" gives 25x
cents, one-quarter of what person "x" gives.

You could work the problem as follows: x + x/2 + x/4 = 525, 4x + 2x + x = 525 * 4 = 2100,
2100/7 = 300, x = 300 and x is in dollars.

 

[Marcelo Arevalo]

Maybe this will help:

Let x=x= amount donated by X
1/4x=0.25x= amount donated by y
1/2x=0.50x= amount donated by z