How do I set this up and how do I solve:
The sum of two numbers is 20 The difference between 3 times the larger number and twice the smaller number is 40. What is the larger number?
let the larger be x
let the smaller be 20-x
Now just translate ...
three times the larger ---> 3x
twice the smaller ---> 2(20-x)
that "difference" is 40
3x - 2(20-x) = 40
3x - 40 + 2x = 40
5x = 80
x = 16
the larger is 16
(the smaller is 4)
Reiny, thank you so much. You broke it down so it was easy to understand.
To solve this problem, we need to set up a system of equations and then solve for the unknown values. Let's call the larger number "x" and the smaller number "y."
The first piece of information from the problem states that the sum of two numbers is 20. We can write this as an equation:
x + y = 20 (Equation 1)
The second piece of information states that the difference between 3 times the larger number and twice the smaller number is 40. We can write this as another equation:
3x - 2y = 40 (Equation 2)
Now we have a system of equations to solve simultaneously. There are several methods to solve this system, such as substitution, elimination, or graphing. Let's use the substitution method.
Step 1: Solve Equation 1 for x:
x = 20 - y
Step 2: Substitute x in Equation 2 with 20 - y:
3(20 - y) - 2y = 40
Step 3: Simplify and solve for y:
60 - 3y - 2y = 40
60 - 5y = 40
-5y = 40 - 60
-5y = -20
y = (-20)/(-5)
y = 4
Step 4: Substitute y = 4 back into Equation 1 to find x:
x + 4 = 20
x = 20 - 4
x = 16
Therefore, the larger number is 16.
To set up this problem, we created a system of equations based on the given information. Then, we solved the system of equations using the substitution method to find the values of x and y.