The sum of two numbers is 133.Four times the smaller of the two numbers equals three times the greater number.

Question

How do I find the numbers?
I am having a hard time trying to figure these out.
Please show me the steps to do this!!

Answer 1

x + y = 133 therefore x = 133 - y

assuming that x is the smaller of the two (it doesn't matter if you pick x or y),
4x = 3y

Now you can use the first equation to solve the second:
4 (133 - y) = 3y
532 - 4y = 3y
532 = 7y
76 = y
and x = 133 - y, so x = 133 - 76
x = 57

57 and 76 are your numbers.

Answer 2

1. Sum of 2 numbers is 133: write an equation with two different variables:
x + y = 133

2. 4 times the smaller of the two numbers equals 3 times the greater number. Write another equation, using the same variables as above. Just "assume" one of the variables will be the smaller. I'm going to assume x is the smaller number:
4x = 3 y

3. Using the equation from #2, solve for x:
* divide both sides by 4 and the equation becomes:
x = 3/4 y

4. Substitute 3/4y for "x" in the equation from #1 and solve for y:
3/4y + y = 133
*multiply everything by 4/1 to get rid of the fraction:
3y + 4y = 532
* combine like variables
7y=532
* divide both sides by 7 to isolate the y:
y = 76
5. Substitute 76 for y in the equation from #1 and solve for x:
x + 76 = 133
*subtract 76 from both sides to find x:
x = 57

6. So your answer is x=57 and y=76

7. Check your answer by substituting these numbers in both the orginal equations and see if the equations are true:
Eq. #1: x + y = 133
57 + 76 = 133 --> true
Eq. #2: 4x = 3y
4*57=228
3*76=228 --> true

Because both of these statements are true, you know the answer of x=57, y=76 is correct.

Answer 3

Suppose x is smaller number and y is larger.
Then you have to write the given data.
The data here is
x+y=133
4*x=3*y
=> x=(3/4)y
substitute the above equation in
x+y=133
=> y(1+3/4)=133
=> y=76, x=57.

Answer 4

Use the wording to set up an algebraic equation...

The sum of two number is 133. (sum means +, and is means =) so...

x + y = 133 (where x and y are your numbers)

then, the other equation is:

4x = 3y (the equation is whats important as it will decide which is smaller and which is larger... the wording is just to confuse you)

so, you have two equations:

x + y = 133 and,
4x = 3y

now you can solve by substitution.

y = 4x/3 so,

x + 4x/3 = 133

7x/3 = 133

x = (3/7)*133 = 57 and since 4x = 3y and therefore y = 4x/3...

y = (4/3)*57 = 76...

So, x = 57 and y = 76.

Answer 5

Let the numbers be x and y and let x be the smaller one
give x + y = 133
and 4x = 3y .
so x = 3/4 y
tha makes x + y = 3/4 y + y = 133
so multiply all the terms by 4 w eget
3y + 4y = 4times 133
so 7y = 4times 133
so y = 4*133/7 which gives y = 76 and x as 57

Answer 6

Let x = smaller number
Then 133-x = larger number
4x = 3(133-x)
4x = 399 -3x
7x = 399
x = 57 = smaller number
133-x = 76 = larger number

This is much easier than using two variables.

Answer 7

Let a be the smaller number, and b be the larger number.

a + b = 133
4a = 3*b

Solving for a.

b = 133 - a
4a = 3 * (133 - a)
4a = 399 - 3a
7a = 399
a = 399/7 = 57

solving for b
b = 133 - 57
b = 76

So the larger number is 76 and the smaller 57.

Answer 8

Use a and b for the unknowns:

a + b = 133 (1)
4a = 3b (2)

From (2), b = 4a / 3

Substitute into (1):

a + (4a / 3) = 133
7a / 3 = 133
7a = 399
a = 57

Substitute into (1):

57 + b = 133
b = 76

Substitute a and b into (2) to check:

4*57 = 3*76
288 = 288

Answer 9

1) S + P = 133 , 4S = 3P so
2) 4S - 3P = 0
| (1) (1) (133)| = after row reduction S = 57, P=76
| (4) (-3) (0) |
(this was linear algebra)
Without Linear algebra
multiply equation 1) by 4 and subtract the two
4S + 4P = 532
-(4S - 3P = 0 )
-----------------------------
7P = 532
P = 76 now plug in P
S + 76 = 133
S = 57 !!!!!

Answer 10

x + y= 133
4x = 3y ..... y=4/3x

x + 4/3x = 133
7/3x = 133
7x = 399
x = 57 ........ y = (57)(4/3) = 76