The sum of two numbers is 80. The ratio of those two numbers is 3:5 . Find the larger number.
the numbers are 3x and 5x.
so, add them up, solve for x, and ...
is it 8x
Can you help ms.sue with this one.
well, yes. The next step is to use their sum to actually find x's value:
8x=80
x=10
Now, you can get the two numbers, once you know x.
To find the solution, you can use algebraic equations. Let's call the two numbers "x" and "y", with "x" being the larger number.
According to the problem, we are given two pieces of information. First, the sum of the two numbers is 80, so we can write the equation as x + y = 80. Second, the ratio of the two numbers is 3:5, which can also be written as x/y = 3/5.
To solve this system of equations, we have a few options. One approach is to use substitution:
1. Solve one equation for one variable (in this case, y) in terms of the other variable (x). From the second equation, we can rewrite it as y = (5/3)x.
2. Substitute the value of y in the first equation with (5/3)x: x + (5/3)x = 80.
3. Combine like terms to simplify the equation: (8/3)x = 80.
4. Multiply both sides of the equation by 3/8 to isolate x: x = (3/8) * 80.
5. Calculate the value of x: x = 30.
6. Substitute the value of x back into the equation for y to find y: y = (5/3) * 30 = 50.
Thus, the larger number is 50.