Question

1. Set up the following word problem as an equation and solve. Then write your answer as a complete sentence. The ratio of two numbers is 3 to 5. Their sum is 136. Find the two numbers.

Answer 1

If x is your first number and y is your second number then x/y = 3/5. Also, x+y = 136. If you find one variable first it is easier to solve. To find y, solve for x in one equation and input it into the other. For example, in x/y = 3/5, x = (3/5)y. This is because you cancel out y on the first side by multiplying and you get it on the other side. Now input x = (3/5)y into x+y=136. This looks like ((3/5)y)+y = 136. Combine like terms. 1 and (3/5)y equals 136. Another way of writing this is
(8/5)y = 136. Isolate the variable by multiplying 5/8. This cancels out 8/5 on the left and solve for y. The answer is y = 85. Plug this into one of your equations and solve for x. For example, x+y = 136 is now x+(85) = 136. Isolate x by subtracting 85 on both sides. This creates x = 51.
The two numbers are 51 and 85.