[Video] Q6: Last week raul worked 11 more hours than angelica. if they worked a combined total of 59 hours, how many hours did angelica work last week?

Explanation for Question 6 From the Math (Calc) Section on the Official Sat Practice Test 4

So now we're looking at question number six, 2 which says that last week role worked more than 11 or 11 hours more 3 rather than Angelica. And if they worked a combined total of 59 hours, 4 how many hours that Angelica worked last week. 5 And so what we need to be able to see here is first that 6 we're going to have two variables, right? We can maybe say are for Raul 7 and a Fran Gelica and we can also create two equations, 8 right? Because if we see that Raul worked 11 more hours than Angelica, 9 then Raul should be equal to Angelica's hours, 10 plus 11, right. Angelica, and then 11 more. 11 And then we also see that they had a total. 12 So if we combine them together a 59 hours, 13 so I have two equations, I have two variables. 14 This is the perfect setup for a systems of equations problem. 15 And it's also perfectly set up so that we can solve it by substitution, 16 because I can simply take this information right here, 17 plug it in for R and then solve for a, 18 which is what I'm interested in. Right. Cause I want to know the hours 19 that Angelica works. So I'll rewrite this equation here, 20 but instead of writing R I'll write a plus 11, 21 I'll substitute that in and that's equal to 59. 22 So now if I'm solving for a, another good step here would be to 23 combine like terms the a and the a, which gives me two, 24 a plus 11 is equal to 59. 25 And so to solve for a, I need to subtract 11 from both sides, 26 which will give me two a, is equal to 48, 27 right? Yup. And then if I divide both sides by 2 48 divided by two 28 that's 24, so Angelica then worked 24 hours per week making 29 our answer to six.