Four numbers have a total of 92. The first number is twice the second number and the third is 4 more than the sum if the first two. The fourth number is 3 less than the difference of the first two numbers. What are the numbers?
Have you done any work on this? You are givenfour equations in the text, with four unknowns.
Im the worst person in the world when it comes to math.
To solve this problem, we can use algebraic expressions and equations.
Let's assign variables to represent the unknown numbers. Let:
- The second number be "x"
- The first number be "2x" (since it is twice the second number)
- The third number be "2x + x + 4" (since it is 4 more than the sum of the first two)
- The fourth number be "(2x) - x - 3" (since it is 3 less than the difference of the first two numbers)
Now, we can set up an equation to represent the given information:
(2x) + x + (2x + x + 4) + (2x - x - 3) = 92
Simplifying the equation:
6x + 1 = 92
Subtracting 1 from both sides of the equation:
6x = 91
Dividing both sides by 6:
x = 15.167
Since the numbers are given as whole numbers, we can disregard the decimal portion. So, x ≈ 15.
Now, we can substitute x = 15 into the equations to find the values of the other numbers:
First number (2x): 2(15) = 30
Second number (x): 15
Third number (2x + x + 4): 2(15) + 15 + 4 = 49
Fourth number ((2x) - x - 3): (2(15)) - 15 - 3 = 24
Therefore, the four numbers are: 30, 15, 49, and 24.