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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

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3 Answers

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