The sum of two numbers is 15. Four times the smaller number is 60 less than twice the larger number. What is the larger number?
If you could help me I would really appreciate it.
To solve this problem, let's assign variables to the two numbers.
Let:
- x be the smaller number
- y be the larger number
We are given two pieces of information:
1. The sum of the two numbers is 15:
x + y = 15
2. Four times the smaller number is 60 less than twice the larger number:
4x = 2y - 60
Now we can solve these equations simultaneously to find the values of x and y. Here's how:
Step 1: Solve equation (1) for x:
x = 15 - y
Step 2: Substitute the value of x from step 1 into equation (2):
4(15 - y) = 2y - 60
Step 3: Simplify and solve for y:
60 - 4y = 2y - 60
60 + 60 = 2y + 4y
120 = 6y
Step 4: Solve for y:
y = 120 / 6
y = 20
Therefore, the larger number is 20.
Sure! Let's solve this problem step by step.
Step 1: Define the two numbers
Let's assume the larger number is 'x' and the smaller number is 'y'.
Step 2: Write down the given information
According to the problem, the sum of the two numbers is 15:
x + y = 15
Also, four times the smaller number is 60 less than twice the larger number:
4y = 2x - 60
Step 3: Simplify the equations
The first equation, x + y = 15, is already simplified.
To simplify the second equation, we can divide both sides by 2:
2y = x - 30
Step 4: Solve the system of equations
We have two equations:
x + y = 15 (Equation 1)
2y = x - 30 (Equation 2)
We can solve this system by substitution or elimination. Let's use the substitution method.
From Equation 2, we can isolate x:
x = 2y + 30
Now substitute this expression for x in Equation 1:
(2y + 30) + y = 15
Combine like terms:
3y + 30 = 15
Subtract 30 from both sides:
3y = 15 - 30
3y = -15
Divide both sides by 3:
y = -15/3
y = -5
Step 5: Find the larger number
We found the smaller number 'y' to be -5. Now substitute this back into either equation to find the larger number 'x':
x + (-5) = 15
x - 5 = 15
Add 5 to both sides:
x = 15 + 5
x = 20
Therefore, the larger number is x = 20.
You can check your answer by substituting the values of x and y back into the given equations to see if they satisfy both equations.
Thank you Steve!
just put the words into math:
x+y=15
4x = 2y-60
Now just solve the system for y.