the sum of two numbers is 17, the difference between the larger number and three times the smaller is 4, find the numbers!
let the larger be x
then the smaller is 17-x
x - 3(17-x) = 4
x - 51 + 3x = 4
4x = 55
x = 13.75
the larger is 13.75 , and the smaller is 3.25
Check:
is 13.75+3.25 = 17 ? YES
the larger ---- 13.75
3 times the smaller -- 9.75
Is that difference equal to 4 ? YES
all is looking good
To solve this problem, we can set up a system of equations based on the given information.
Let's call the larger number "x" and the smaller number "y".
From the given information, we have:
Equation 1: x + y = 17 (the sum of two numbers is 17)
Equation 2: x - 3y = 4 (the difference between the larger number and three times the smaller is 4)
Now we have a system of two equations with two variables. We can solve it using either substitution or elimination.
Let's use the substitution method:
First, solve Equation 1 for x:
x = 17 - y
Now substitute this value of x into Equation 2:
(17 - y) - 3y = 4
Simplify the equation:
17 - y - 3y = 4
17 - 4y = 4
Now solve for y:
-4y = 4 - 17
-4y = -13
y = -13 / -4
y = 13 / 4 = 3.25
Now substitute the value of y back into Equation 1 to find x:
x + 3.25 = 17
x = 17 - 3.25
x = 13.75
So, the numbers are x = 13.75 and y = 3.25.