the sum of two numbers is 21. The first number is 2/5 of the second number. what are the numbers?
Help, I have been trying to figure this out for two hours and my eyes are starting to cross!! Please and Thank you.
(2/5)x + x = 21
(7/5)x = 21
x = 15
The two numbers are
6 and 15
Let's solve this problem step by step.
Step 1: Understand the problem.
We are given two pieces of information:
- The sum of two numbers is 21.
- The first number is 2/5 (or 2 out of 5 parts) of the second number.
Step 2: Assign variables.
Let's use variables to represent the unknown numbers. We can choose any letters, but let's use "x" for the first number and "y" for the second number.
So, we have:
- The first number: x
- The second number: y
Step 3: Set up equations.
We need to translate the information given into equations.
Based on the problem statement:
- The sum of the two numbers is 21. This can be written as:
x + y = 21
- The first number is 2/5 of the second number. This can be written as:
x = (2/5) * y
Step 4: Solve the equations.
We have a system of two equations:
x + y = 21 (Equation 1)
x = (2/5) * y (Equation 2)
To solve this system, we can substitute Equation 2 into Equation 1:
(2/5) * y + y = 21
Now, let's solve for y:
(2/5) * y + y = 21
(2y/5) + (5y/5) = 21
(2y + 5y)/5 = 21
(7y)/5 = 21
7y = 21 * 5
7y = 105
y = 105/7
y = 15
Now that we know the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 15 = 21
x = 21 - 15
x = 6
Step 5: Check the solution.
Let's check if our solution is correct:
- The sum of the two numbers is 21: 6 + 15 = 21 (Correct)
- The first number is 2/5 of the second number: 6 = (2/5) * 15 (Correct)
So, the two numbers are 6 and 15.