The larger of two numbers is 5 less than twice the smaller number. The sum of four times the larger and twice the smaller number is 100. If x is the smaller number, which equation below determines the correct value of x?
A) 2(2x + 5) + 4x = 100
B) 2(2x – 5) + 4x = 100
C) 4(2x + 5) + 2x = 100
D) 4(2x – 5) + 2x = 100
smaller number ---- x
"The larger of two numbers is 5 less than twice the smaller number"
---> 2x - 5
Now just translate:
"The sum " ---> +
"The sum of [four times the larger] and [twice the smaller number]
---> 4(2x-5) + 2x
" is 100" ---> = 100
4(2x – 5) + 2x = 100
To solve this problem, we need to write equations based on the given information and then solve for x.
Let's assign variables to the two numbers. Let x be the smaller number and y be the larger number.
According to the problem, the larger number (y) is 5 less than twice the smaller number (x). This can be expressed as y = 2x - 5.
The sum of four times the larger number (4y) and twice the smaller number (2x) is 100. This can be written as 4y + 2x = 100.
Now we have two equations:
1) y = 2x - 5
2) 4y + 2x = 100
Substituting the first equation into the second equation, we get:
4(2x - 5) + 2x = 100
Simplifying this equation gives us:
8x - 20 + 2x = 100
10x - 20 = 100
10x = 120
Dividing both sides of the equation by 10, we find that x = 12.
Therefore, the correct equation to determine the value of x is:
D) 4(2x – 5) + 2x = 100.