Word problem:
The sum of two numbers is 26.4. One number is five times the other number. Find the numbers.
It's probably:
x+y=26.4
x=5y
But, I could be wrong and I don't know where to go from there.
5y + y = 26.4
6y = 26.4
y = 26.4/6
y = 4.4
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Let's see if that's right.
4.4 + (5*4.4) = 26.4
4.4 + 22 = 26.4
Right!
thanks! that's really helpful
You're welcome.
Remember that you had the right start. :-)
You started the problem correctly by setting up two equations to represent the given information. Let's go through the steps to find the values of the two numbers.
1. Begin with the equations you wrote:
x + y = 26.4 (Equation 1)
x = 5y (Equation 2)
2. We can solve the system of equations using substitution. Start by solving Equation 2 for x.
Substitute x = 5y into Equation 1:
5y + y = 26.4
3. Combine like terms:
6y = 26.4
4. Divide both sides of the equation by 6 to isolate y:
y = 26.4 / 6
y = 4.4
5. Now that we have the value of y, substitute it back into Equation 2 to find x:
x = 5(4.4)
x = 22
6. Hence, the two numbers are x = 22 and y = 4.4.
To verify our answer, let's check if the sum of these numbers is indeed 26.4:
22 + 4.4 = 26.4
Therefore, the solution is correct. The two numbers are x = 22 and y = 4.4.