Each week John earns X dollars per hour for the first 40 hours that he works that
week and Y dollars for each additional hour. How much does John earn per hour for
the first 40 hours?
(2) If John works 45 hours in a week, he earns a total of $570 that week
I think the answer should be C because from the second equation we can get 40X+5Y=570 and we can substitute from first equation Y=15X =40x+75x=570
hence we can get the value for x
Please let me know If am in the right direction ...
You're reasoning is right on and illustrates how to apply the most powerful tool in your DS arsenal: the number of equations vs number of unknowns rule.
The rule states:
For a system containing n variables, one requires n distinct linear equations to solve the system.
Looking for applications of this rule on DS questions will allow you to quickly and confidently select the correct answer without doing much math - we love it when that happens!
For example, here's how we could have analyzed this question:
Q stem: 3 variables (X, Y, amount earned), 1 equation. What do we need to solve? Either 2 more distinct linear equations (that introduce no new variables) or 1 special equation that eliminates both undesired variables.
(An important corollary to the rule is that if you're only solving for part of the system, you may not need the standard number of equations; similarly, if you're solving for a relationship among variables instead of the actual values of variables, you can often solve with fewer equations.)
1) one distinct linear equation, no new variables: insufficient.
2) one distinct linear equation, no new variables: insufficient.
Together: 2 distinct linear equations, no new variables: sufficient - choose (C).
Note that we didn't need to translate the equation from (2) - we just needed to be sure that it was different from the other two equations, didn't introduce any new variables and was linear (i.e. no exponents other than 1 attached to our variables).
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