The sum of two numbers is 76. The larger is 11 less than 3 times the smaller number. Find the smaller number,?

You're setting up a system of equations, which then can be solved to find the answer:

Let:
x and y = your two numbers.

The sum of two numbers is 76:

x + y = 76

The larger is 11 less than 3 times the smaller:

x = 3y - 11

Now you have two unknowns and two equations, solveable. I have x in terms of y already in equation 2, so we can substitute (3y - 11) for x in equation 1 and solve for y:

x + y = 76
(3y - 11) + y = 76
4y - 11 = 76
4y = 87
y = 87/4

Now we can solve for x:

x + y = 76
x + 87/4 = 76
x = 217/4

The smaller of the two is 87/4

smaller number = 21.75
larger number = 54.25

x + y = 76
y = 3x - 11

x + 3x - 11 = 76

4x = 87

x = 21.75

(3x-11)+x=76
solve for x

First you need to figure out the formula to use. "The sum of two numbers is 76" tells you you are dealing with addition. "The larger number is 11 less than 3 times the smaller number, find the smaller number?" We need to know the smaller number so we will call it "X". The larger number would then be 3 times X minus 11. We know that 3 times X minus 11, plus X equals 76. Written like this:

(3x-11) + x = 76

Now we just solve for X.

4x-11=76
4x=76+11
4x=87
x= 87/4
x= 21.75

Now we check it by plugging our new X value into the formula to make sure it's right:
(3(21.75)-11)+ 21.75 =
(65.25-11) + 21.75 =
54.25 + 21.75 = 76
and it is The smaller number is twenty-one and three-quarters.

x = the smaller number

x + (3x - 11) = 76
x + 3x - 11 = 76
4x = 76 + 11
4x = 87
x = 87/4 (21.75)

∴ the smaller number is 87/4 (21.75).

1) x + y = 76
2) x = 3y - 11
3) (3y - 11) + y = 76
4y - 11 = 76
4y = 87
y = 87/4
4) x + 87/4 = 76
x = 217/4

i can't wait to see the answer! I just can't remember how to do these equations!!! Good luck!

Call the two numbers a and b.

"the sum of the two numbers" means that if you add them up you get 76:

a + b = 76

If a is the big one and b is the small one, then the second bit means that:

a + 11 = 3b

These are two equations which can be solved simultaneously. Rearranging the first gives:

a = 76 - b

Then whenever you see an "a" in the second equation you can replace it with the formula 76 - b.

76 - b + 11 = 3b

Then solve as normal

87 = 4b

b = 21.75

X + 3X=76

Solve for x,

4x=76
x=19...the smaller number is 19