So I solved this problem but, strange as it sounds, I don't know how to do the work.
Here's the question: One number is eight less than another number. The sum of the numbers is eighty. Find both numbers.
Here's what I've got:
y-8=x
x+y=80
x=36
y=44
I won't get credit unless I show the "correct" work. Can you help me please?
y - 8 = x
x + y = 80
Substitute y-8 for x in the second equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.
y-8=x
x+y=80
Substitute
y - 8 + y = 80
2y = 88
y = 44
44 - 8 = x
36 = x
Of course, I can help you. To show the work for solving the problem "One number is eight less than another number. The sum of the numbers is eighty. Find both numbers," you can follow these steps:
1. Assign variables: Let x be the first number and y be the second number.
2. Translate the problem into equations.
a) "One number is eight less than another number" can be represented as y = x - 8.
b) "The sum of the numbers is eighty" can be written as x + y = 80.
3. Now you have a system of equations:
y = x - 8 (Equation 1)
x + y = 80 (Equation 2)
4. You can solve this system by substitution, elimination, or any other method of solving systems of equations.
Let's use substitution here:
- From Equation 1, you know that y = x - 8.
- Substitute this value of y into Equation 2: x + (x - 8) = 80.
- Simplify: 2x - 8 = 80.
- Add 8 to both sides: 2x = 88.
- Divide both sides by 2: x = 44.
5. Now that you have the value of x, substitute it back into Equation 1 to find y:
y = 44 - 8.
Simplify: y = 36.
6. Thus, the numbers are x = 44 and y = 36.
Now, you can show these steps as your work and explain how you arrived at the solution. Good luck!