Sum of two numbers is 21. Three times the larger is equal to four times the smaller. Find them

Question

hi, is there is a special trick to solving these word problems? I'm having a bit of difficulty with the words.

Answer 1

Hi Alex, no tricks are involved. Let x be one number and y the other number. Equation 1 is:

 

x + y = 21

 

Equation 2:

 

3 * x = 4 * y, it does not matter which one we pick to be the larger or smaller number.

 

solve equation 2 for x:

 

3x = 4y

 

Divide both sides by 3:

 

x = 4 / 3 * y

 

Substitute for x in equation 1:

 

4 / 3 * y + y = 21

 

Multiply entire equation by 3 to clear the fraction:

 

4y + 3y = 63

 

7y = 63

 

Divide both sides by 7:

 

y = 9

 

Substitute for y in equation 1:

 

x + 9 = 21

 

Subtract 9 from both sides:

 

x = 12

 

One number is 9 and the other number is 12.

 

Questions?