# An equation for an algebra word problem

1. May 8, 2017

### mech-eng

1. The problem statement, all variables and given/known data
Suppose that b is 20% more than a, c is 25% more than b, and d is k% less than c. Find k such that a=d

2. Relevant equations
a=d; b=1.2a; c=1.25b=1.5a

3. The attempt at a solution
1. a=$\frac{c}{15 }$=d=$\frac{100c-k}{100}$
2. By multiplication of extremes and means we get 100c=150c-15.k
3. 50c=1.5k
4. Again simplifying k=33.3c

I have tried above solution but I think something is incorrect because k should be a number not a ratio in terms of c.
I don't latex well enough and it seems that step 1 is not seeming properly, too small symbols.
Source: Algebra and Trigonometry by Keedy Bittinger.
Thank you.

2. May 8, 2017

### SammyS

Staff Emeritus
You have a typo and an error in multi-equation #1.

For one, $\ \displaystyle a=\frac{c}{1.5} \$. (Missed the decimal point.)

More importantly the last part is in error.
$\ \displaystyle \frac{100c-k}{100} \$​
is incorrect. $\ k\$ must also multiply $\ c\$.

3. May 8, 2017

### mech-eng

But if $d$ is $k%$ less than $c$, does not this mean $\frac{c}-k}{100}$ and isn't it $\frac{100c-k}{100}$?

And would you please explain why percent sign not appear in this code?

Thank you.

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Last edited: May 8, 2017
4. May 8, 2017

### Ray Vickson

You need
$$d =\left( 1 - \frac{k}{100} \right) c$$

5. May 8, 2017

### mech-eng

$$d =\left( 1 - \frac{k}{100} \right) c$$=$\frac{c}{1.5}$

$50c=15ck$

and k=3.333

Would you please write above in the proper latex form?

Thank you.

6. May 8, 2017

### UsableThought

@mech-eng, I suggest you check your answer of $k = 3.333\%$ against your initial set of equations $a=d; b=1.2a; c=1.25b$.

Also, although percentages proper are expressed as $x/100$, it's easier & faster during calculation to assume 1 = 100%; thus instead of $$d = \left(1 - \frac{k}{100}\right) c$$ you can work more simply with $d = (1 - k)c$. For that matter you can substitute a temporary value for that expression and do the subtraction later on.

Last edited: May 8, 2017
7. May 8, 2017

### SammyS

Staff Emeritus
That looks proper to me.

Mathematically, it's equivalent to

$\ \displaystyle d = \left(\frac{100-k}{100}\right) c$

8. May 8, 2017

### UsableThought

I think the OP was referring to the part of his comment that wasn't already formatted in LaTeX.

Last edited: May 8, 2017
9. May 8, 2017

### mech-eng

$\ \displaystyle d = \left(\frac{100-k}{100}\right) c=\frac c {15}$

I added the right side but is it proper. I didn't used symbols such as \left and \right.
The following is what I added there. But it is not the same when it is on the right side. Would you please explain this?
$\frac c {15}$

Thank you.

10. May 8, 2017

### SammyS

Staff Emeritus
Proper in what way?

You dropped the decimal point from 1.5 again, otherwise, it looks right math-wise .

By the way: for % symbol in LaTeX, use \ suffix as in \%.

$7\%$ or $k\%$

11. May 8, 2017

### mech-eng

Sorry. Question is solved. But look the Latex. Their size of the c/15 parts are different.

Thank you.