Before their promotions, Taryns salary was 20% higher than her

Question

Before their promotions, Taryn’s salary was 20% higher than her husband’s. Taryn’s salary then tripled, and the dollar increase in her salary tripled the increase in her husband’s salary.

If the difference between their new salaries is $7,200, what is their combined salary now?

A. $19,200
B. $21,600
C. $24,000
D. $25,000
E. $28,800

A. $19,200
B. $21,600
C. $24,000
D. $25,000
E. $28,800

Budhaditya_Saha · Answer

Set variables (before promotion)
Let husband’s salary = H
Taryn’s salary is 20% higher:
T=1.2H

After promotion
Taryn’s salary  triples :
Tnew=3T=3(1.2H)=3.6H

Increase in Taryn’s salary:
3.6H−1.2H=2.4H
 
Use the key condition:
 Taryn’s increase =  3 × husband’s increase 
So husband’s increase:
=2.4H/3=0.8H

Thus, husband’s new salary:
Hnew=H+0.8H=1.8H
 
Using the final difference
Difference between new salaries = 7200:
3.6H−1.8H=7200.
Thus, H=4000
 
The combined new salary
3.6H + 1.8H
Total: 14400+7200=21600
 
Thus, Option B.

kevincan · Answer

This question is tailor made for scaling : what would be a nice number to pick for Taryn’s initial salary?

egmat · Answer

Let's break this down step by step.

Step 1: Set up variables. 
Let the husband's original salary =  H .
Taryn's original salary was  20%  higher, so Taryn's original salary =  1.2H .

Step 2: Find their new salaries. 
Taryn's salary tripled: New Taryn =  3  ×  1.2H  =  3.6H .
Taryn's dollar increase =  3.6H  -  1.2H  =  2.4H .

Now here's the tricky sentence: "the dollar increase in her salary tripled the increase in her husband's salary." This means Taryn's increase was  3  times the husband's increase.
So husband's increase =  2.4H  /  3  =  0.8H .
Husband's new salary =  H  +  0.8H  =  1.8H .

Step 3: Use the difference to find H. 
Difference between new salaries =  3.6H  -  1.8H  =  1.8H .
We're told this equals  $7,200 .
 1.8H  =  $7,200 
 H  =  $4,000 .

Step 4: Find combined new salary. 
Taryn's new salary =  3.6  ×  $4,000  =  $14,400 .
Husband's new salary =  1.8  ×  $4,000  =  $7,200 .
Combined =  $14,400  +  $7,200  =  $21,600 .

Answer: B

The most common mistake here is misreading the sentence about the increases.  Some students think the husband's increase tripled Taryn's increase (getting it backwards), which would give a wrong answer. Always read carefully: "her salary tripled the increase in her husband's" means Taryn's increase =  3  × husband's increase.

Before their promotions, Taryns salary was 20% higher than her

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