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# three times the larger of two numbers is equal to four times the smaller.the sum of the numbers is 21

i dont know how to set up the equations

### 3 Answers by Expert Tutors

Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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Since the sum of the two numbers is 21,
let x be one number and 21-x be the other.

x + (21-x) = 21

Since "three times the larger of two numbers is equal to four times the smaller"...
3x = 4(21-x)

3x = 84 -4x
7x = 84
x = 12

Since x = 12, 21-x = 21-12 = 9.

Larger number is 12, smaller number is 9.

Note that if you said:
3(21-x) = 4x
63 - 3x = 4x
63 = 7x
x = 9, and 21-x = 21-9 = 12

12 would still be the larger number and 9 would still be the smaller.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Ruaai;
three times the larger of two numbers is equal to four times the smaller.the sum of the numbers is 21

x=smaller number
y=larger number

x+y=21

3y=4x

We will begin with either equation.
The first is the easiest...
x+y=21
Let's isolate y...
y=21-x

The second equation...
3y=4x
Let's substitute...
3(21-x)=4x
63-3x=4x
Let's isolate x by adding 3x to both sides...
63-3x+3x=4x+3x
63=7x
Let's divide both sides by 7...
63/7=7x/7
9=x

21-9=12=y

Let's check our work...
3y=4x
3(12) ? 4(9)
36=36

Barbara D. | MATH! - Middle/High school/SAT/ACT. Patient/experienced!MATH! - Middle/High school/SAT/ACT. Pati...
5.0 5.0 (108 lesson ratings) (108)
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Since larger number is based off of smaller number, start with smaller number.

smaller number = x

Since we only know larger is "more by some amount" call it:

larger =x +y

1st equation:
3 times larger IS 4 times smaller
3(x+y)            =  4(x)

now, distribute:
3x+3y   =    4x
That's equation 1.

sum of 2 numbers is 21.
so,   larger +smaller =21