Question

If 8x + 8y = 4 and 4x + 2y = 12, what is the value of x?
Responses

Answer 1

Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have all together when they started collecting?
Responses
A 6
B 3
C 7
D 14

Answer 2

To find the value of x, we can use the second equation to solve for y in terms of x:

4x + 2y = 12
2y = 12 - 4x
y = 6 - 2x

Then we substitute this expression for y into the first equation:

8x + 8y = 4
8x + 8(6 - 2x) = 4
8x + 48 - 16x = 4
-8x + 48 = 4
-8x = -44
x = 5.5

Therefore, the value of x is 5.5.

Answer 3

Let the number of rare coins they had when they started collecting be "x".

Miguel has been collecting 5 coins each week, so he has collected (38 - x) coins in total.
Grace has been collecting 3 coins each week, so she has collected (24 - x) coins in total.

We know that Miguel and Grace had the same number of rare coins when they started collecting, so:

38 - x = 24 - x
14 = x

Therefore, they had a total of x = 14 rare coins when they started collecting.

The answer is (D) 14.