Two numbers have a ratio of 7:5. The sum of the two numbers is 960. What are the two numbers?
2800
To find the two numbers, let's use the given ratio of 7:5.
Step 1: Set up the equation.
Let's assume the two numbers are 7x and 5x, where x is a common factor.
So, the equation becomes:
7x + 5x = 960
Step 2: Combine like terms.
Combining the x terms, we have:
12x = 960
Step 3: Solve for x.
Divide both sides of the equation by 12:
x = 960 / 12
x = 80
Step 4: Find the two numbers.
Multiply x by the ratios to find the actual numbers:
7x = 7 * 80 = 560
5x = 5 * 80 = 400
Therefore, the two numbers are 560 and 400.
To find the two numbers, we first need to understand the concept of ratio.
A ratio compares two numbers, quantities, or values and shows the relationship between them. In this case, the ratio of the two numbers is given as 7:5.
Let's assume the two numbers are 7x and 5x, such that their ratio is 7:5. Here, x is a common factor used to scale the numbers.
According to the problem, the sum of the two numbers is 960. So we can write the equation:
7x + 5x = 960
Simplifying the equation, we have:
12x = 960
Now, to solve for x, we divide both sides of the equation by 12:
x = 960 / 12
x = 80
Now that we have the value of x, we can substitute it back into our assumed numbers:
7x = 7 * 80 = 560
5x = 5 * 80 = 400
So the two numbers are 560 and 400.
Let the two number be 7x and 5x
7x + 5x = 960
solve for x, and sub back into my definitions