- #1

Mindscrape

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The average weekly salary of 12 workers and 3 managers in a factory was $600. A manager whose salary was $720 was replaced with a new manager, then the average salary of the team fell to $580. What is the salary of the new manager?

So basically we start with (from the first sentence)

$$\frac{tw+tm}{15}=600$$

where tw represents total worker salary and tm represents total manager salary. Now the second sentence says

$$tm=m1+m2+720$$

so the first equation is now (having multiplied out the 15 from before) -- also label this eqn1

$$tw+m1+m2+720=9000$$

continuing with info from the second sentence, we get the second equation for the newly decreased average as

$$\frac{tw+m1+m2+m3}{15}=580$$

now simplifying gives -- and labeling this eqn2

$$tw+m1+m2+m3=8700$$

subtract the two equations (eqn1-eqn2)

$$720-m3=300$$

for the grand finale...

$$m3=420$$