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[High School Math] Percentage limit on portion of total

If I have 100 of x and 100 of y. I want to add them together but y can only be 35% of the total of the two.

z-x+y where y=z*.35 and x=100

z=100+(z*.35)

The formula I was told to use is =x*.35/(1-.35) which produces the solution 53.84 which is 35% of the 153.84 but I don't understand how that formula was created. I'm sure this is basic algebra that I've forgotten but I don't understand the mathematical concept.

I understand that dividing by (1-.35) determines that 35 is 65% of 53.64. But how does finding the percentage of a number and dividing it by the opposite of the initial percentage produce the amount required?

Posted Oct 22, 2017, 12:32 AM UTC · edited

03
wijwijwij•

You're trying to figure how much y you can add to 100 units of x. Let's call that amount y.

You want (y)/(100+y) to be 35%.

(y)/(100+y) = 35/100

Cross multiply.

100y = (100+y)35

100y = 3500 + 35y

100y – 35y = 3500

65y = 3500

y = 3500/65

y = 35/0.65 [I think that's (x * .35) / (1 – 0.35) you were referring to if x = 100.]

y = 53.84

2
HNWOP•

Thank you for the explanation. I'm not sure why someone else down voted your post.

Your setup and steps make a lot more sense to me.

2
wijwijwij•

I think I can draw a connection between the way you were thinking about this and the formula you were told you could use.

You were implying:

z = x + y

That is, z is the total amount after the combination.

y = z * 0.35

This means that y amount is supposed to be 35% of the total amount after the combination.

You put those two things together to get this equation:

z = x + z * 0.35

You know you'll be able to use an amount of 100 as x.

z = 100 + z * 0.35

You can solve this equation for z.

1z – 0.35z = 100

(1 – 0.35)z = 100

z = 100/(1 – 0.35)

But what we're being asked for is y, which as you recall is z * 0.35.

y = z * 0.35

y = 100 * 0.35/(1 – 0.35)

This is the formula you were given, but you've already substituted 100 in for x.

y = x * 0.35/(1 – 0.35)

My conclusion is that every step you were taking was correct, and you just needed to "solve for z" and then use that to represent y to arrive at that formula.

But you didn't have to use that formula. You could just continue your line of reasoning to completion to get the answer:

z = 100/(1 – 0.35) = 100/0.65 = 153.84

Then there are two ways to find y.

y = z – x = 153.84 – 100 = 53.84

Or

y = z * 0.35 = 153.84 * 0.35 = 53.84

3