Problema Solution
3. Abigail found a list of names and salaries. The list of names are: Courtney, Emma, and Rachel. The list of salaries are 39x + 12320, 84x + 17010, and 15310 + 40x. Can you help Abigail figure out everyone's real salary?
A. Courtney earns 15310 + 40x.
B. Rachel earns more money than Emma.
C. Emma makes the least amount of money.
D. Rachel earns $7,390 more than Emma.
E. Emma earns less than Rachel. If Emma earned $49,890 more, Emma would earn more than Rachel.
F. Courtney earns less money than Rachel.
Answer provided by our tutors
If Courtney earns less than Rachel (F.), and Emma makes the least
(C.), then the salaries are as follows:
Rachel > Courtney > Emma
We already know that Courtney earns 15310 + 40x (A.), and Rachel
earns $7,390 more than Emma (D.). Therefore Rachels salaries equation is 7,390
more than Emmas.
Either 39x +12320 +7390 = 84x
+ 17010 or 84x + 17010 +
7390 = 39x + 12320; so we try to solve both:
39x +12320 +7390 = 84x +17010
39x + 85710 = 84x +17010
39x + 85710 - 17010 = 84x
39x + 68700 = 84x
68700 = 84x - 39x
68700 = 45x
68700/45 = x
1526.67 = x (this equation
works with a positive number and we have solved for x)
Or
84x +17010 + 7390 = 39x + 12320
84x + 24400 = 39x +12320
84x + 24400 - 12320 = 39x
84x + 12080 = 39x
12080 = 39x - 84x
12080 = -45x
-28.44 = x (this equation does not work as we know that
salaries are going to be positive amounts)
Now we know that 39x
+12320 +7390 = 15310 + 40x , and that Rachels
salaries equation is 7,390 more than Emmas we know that Rachel makes 84x + 17010, and Emma makes 39x +12320. All that is left is to solve all three
equations since we already know that x = 1526.67
Rachel:
84x + 17010 = 84(1526.67) +17010 = 128240.28 + 17010 = $145,250.28
Courtney:
15310 +
40x = 15310 + 40(1526.67) = $76,376.80
Emma:
39x +12320 = 39(1526.67) + 12320 = $71,860.13