I'm working on a couple of SAT math programs for school, and I have trouble figuring some out.
1. Joe is 3 years younger than Kate. If n represents Nora's age now, what was Kevin's age 4 years ago, in terms of n?
A. N + 7
B. N + 1
C. N - 1
D. N - 4
E. N - 7
2. If (x + y)^2 - (x - y)^2 = 84 and x and y are positive integers, which of the following could be a value of x + y?
A. 10
B. 12
C. 14
D. 16
E. 18
Thanks so much in advance!
1. Not possible to solve. Too many kids named.
2. You have a diference of two squares, it factors to (x+y-x+y)(x+y+x-y) which reduces to 2y*2x=4xy or then solve for x,y
4xy=84
xy=21 and 7 and 3 fit that real nicely.
Sure, I can help you with these SAT math problems!
1. Joe is 3 years younger than Kate. If n represents Nora's age now, what was Kevin's age 4 years ago, in terms of n?
To solve this problem, we need to understand the relationships between the different people's ages. We are given that Joe is 3 years younger than Kate. This means that Joe's age is equal to Kate's age minus 3.
Let's represent Kate's age as k. Therefore, Joe's age would be k - 3.
Now, we are looking for Kevin's age 4 years ago. Let's represent Kevin's age at that time as k-4. So, Kevin's age in terms of n would be (k-4).
Based on the given information, we don't have an explicit relationship between Nora's age (represented as n) and Kevin's age. Therefore, we cannot directly solve for Kevin's age in terms of n. Hence, the answer to this question would be "None of the above."
2. If (x + y)^2 - (x - y)^2 = 84 and x and y are positive integers, which of the following could be a value of x + y?
To solve this problem, we need to simplify the equation and then find possible values for x + y.
Expanding the expression (x + y)^2 - (x - y)^2 using the difference of squares formula, we get:
(x + y)^2 - (x - y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2)
Simplifying and canceling terms, we get:
4xy = 84
Now, we need to find two positive integer values of x and y that satisfy the equation 4xy = 84. Since x and y are positive integers, we can easily determine the possible values.
Dividing both sides of the equation by 4, we get:
xy = 21
The positive integer pairs (x, y) that satisfy xy = 21 are: (1, 21), (3, 7), and (7, 3).
Now, we can check which of the answer choices have x + y equal to one of the possible values we found.
Calculating the sums for each answer choice:
A. 10 = 1 + 9 (x + y can't be 10)
B. 12 = 1 + 11 (x + y can't be 12)
C. 14 = 7 + 7 (x + y can be 14)
D. 16 = 7 + 9 (x + y can't be 16)
E. 18 = 7 + 11 (x + y can't be 18)
Therefore, the answer to this question is C. 14, as it is the only sum of x + y that matches with one of the possible solutions for x and y.
I hope this helps! Let me know if you have any further questions.