If x and y are positive integers, which of the following could be equal to
3x+ 4y?
The answer is 10, but not sure on how to get the answer? Also, is there a short cut to get to the answer without taking a lot of time on the SAT to work this type of problem out?
Thank you
3x + 4y = 10, if x = 2 and y = 1.
This still isn't clear to me because 0 is a positive integer so I could put x=2 and y=0 and get 3x + 4y= 6. The answer is 10 and the answer choices are:
A-6
B-8
C-9
D-10
E-12
To find which value could be equal to 3x + 4y, you can start by substituting different values for x and y and checking if any combination gives you the desired result.
Let's try substituting x = 1 and y = 2:
3(1) + 4(2) = 3 + 8 = 11
This is not equal to 10, so this combination doesn't work.
Let's try substituting x = 2 and y = 1:
3(2) + 4(1) = 6 + 4 = 10
This combination gives us the desired result of 10. Therefore, 10 could be equal to 3x + 4y.
On the SAT, you can save time by utilizing a shortcut. Notice that the coefficients of x and y, which are 3 and 4, have no common factors other than 1. This means that any multiple of their sum will be a possible solution.
Since 3 and 4 are relatively prime, a multiple of their sum can be found by multiplying them together: 3 * 4 = 12.
Therefore, any integer that is a multiple of 12 can be a possible solution. In this case, since we are looking for a sum of 10, which is not a multiple of 12, we can conclude that 10 is not a possible value for 3x + 4y.
To summarize, the shortcut is to find the greatest common factor (GCF) of the coefficients and use it to quickly determine the multiples of their sum.
In this case, the GCF is 1, so any multiple of the sum 3 + 4 = 7 will work. Since 10 is not a multiple of 7, it cannot be a possible value for 3x + 4y.