i dont know how to set up the equations

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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.

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

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

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