Algebra 2
The difference of two numbers is 4. Three times the smaller minus the larger is 10. Find the numbers.
larger --- x
smaller ---- y
x-y = 4 ----> x = y+4
3y - x = 10
sub in the first:
3y - (y+4) = 10
3y - y - 4= 10
2y = 14
y = 7
then x=7+4 = 11
the larger is 11 , the smaller is 7
check: their difference is 4 , check!
3 times the smaller minus the larger is 10
21 = 11 = 10 , check!
my answer is correct
If x is the smaller and y is the larger,
y-x = 2
3x-y = 10
add them up and you get
2x = 12
x=6
so, y=8
Oops. I misread the problem.
To solve this problem, let's represent the two numbers using variables. Let's call the smaller number "x" and the larger number "y". According to the problem, the difference between the two numbers is 4, so we can set up the equation:
y - x = 4 (Equation 1)
The second piece of information tells us that three times the smaller number minus the larger number is equal to 10. We can write this as:
3x - y = 10 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). To solve this system, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From Equation 1, we can rearrange it to express y in terms of x:
y = x + 4
Now we substitute this expression for y in Equation 2:
3x - (x + 4) = 10
Simplifying the equation:
3x - x - 4 = 10
2x - 4 = 10
2x = 10 + 4
2x = 14
x = 14/2
x = 7
We have found the value of x, which is 7. Now, we can substitute this value back into Equation 1 to find the value of y:
y - 7 = 4
y = 4 + 7
y = 11
So, the smaller number is 7 and the larger number is 11.