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?
is "Anonymous" so named because the response is incorrect?
To solve this problem, we'll use a system of two equations with two variables.
Let's assume that the smaller number is x, and the larger number is y.
From the problem, we have 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
We now have a system of equations:
Equation 1: x + y = 15
Equation 2: 4x = 2y - 60
To solve this system, we can use one of several methods, such as substitution or elimination. Let's use the substitution method.
From Equation 1, we can rewrite it as x = 15 - y.
We can substitute this value of x into Equation 2 to solve for y:
4(15 - y) = 2y - 60
Now, let's simplify and solve for y.
60 - 4y = 2y - 60
60 + 60 = 2y + 4y
120 = 6y
Divide both sides by 6:
120/6 = y
y = 20
Therefore, the larger number (y) is 20.
4s = 2L - 60
s = (2L-60)/4
s + L = (2L-60)/4 + L = 15
Solve for L.
s + L = 15 ... s = 15 - L
4 s + 60 = 2 L
substituting ... 60 - 4 L + 60 = 2 L
solve for L
x = larger
15 - x = smaller
Four times the smaller number is 60 less than twice the larger number.
4(15 – x) = 2x - 60
60 - x = 2x - 60
Solve for x