Explanation for Question 9 From the Math (No Calc) Section on the Official Sat Practice Test 7
Question nine says Marissa needs to hire at least 10 staff members for an 2 upcoming project. The staff members will be made up of junior directors who 3 will be paid $640 per week. 4 And senior directors who will be paid $880 per week. 5 Her budget for paying the staff members is no more than $9,700 6 per week. She must hire at least three junior directors and at least one 7 senior director, which of the following systems of inequalities represents the conditions 8 described if X is the number of junior directors and why is the number 9 of senior directors? So we need to set up four different inequalities 10 here. Let's start with this one that we're given right here. 11 So we know that junior director is represented by X makes $640. 12 So we can represent that as 640 X. 13 And that's being added to the price of the senior directors, 14 which is $880 and represented by Y. 15 So we can rewrite that as plus 880 Y that however, 16 uh, the director's budget is no more than $9,700, 17 which means that this amount must be less than or equal to 9,700. 18 And just from that first inequality, 19 we can already eliminate answer choices and which used a greater than sign 20 greater than or equal to sign and Ann's choice, 21 which made the same mistake. Next, 22 we need to figure out how many people total should be higher. 23 Well, it says right here that Marissa needs hire at least 10 staff members. 24 So the number of staff members should be greater than or equal to 10. 25 And the number of staff members is going to be represented by X plus 26 Y cause that's the number of junior directors plus the number of senior directors 27 and I've ever two answer choices left. Only one of them uses the correct 28 inequality, sign, answer, choice B which correctly is written as X plus 29 Y is greater than or equal to 10. 30 So answer choice B is the only possible answer here.