solve math word problem

Question

the larger number of two number is 3less than four times the smaller.  When the smaller number is subracted from the larger, the difference is 6. Find the numbers

Answer 1

Hi Stacy;

the larger number of two number is 3less than four times the smaller. When the smaller number is subracted from the larger, the difference is 6. Find the numbers

x...smaller number

4x-3...larger number

(4x-3)-x=6

Let's combine like terms...

4x-3-x=6

3x-3=6

Let's add 3 to both sides as we proceed to combine like terms and isolate x...

3x-3+3=6+3

3x=9

Let's divide both sides by 3...

(3x)/3=9/3

x=3...smaller number

4x-3=[(4)(3)]-3=12-3=9...larger number

Let's check our work...

9-3=6

6=6

Answer 2

It's important to slowly and accurately translate the words into symbols, and then you can start to solve for the unknowns (the variables):

 

The larger number of the two (x) is (=) 3 less (-3) than 4 times the smaller (4y).

This becomes x = 4y - 3

 

When the smaller number (y) is subtracted from the larger (x) which turns into (x-y), the difference (=) is 6.

This becomes x - y = 6

 

The great part is that either one can be turned into an equation where you have one variable by itself (the x or the y). Then you simply plug in the value of x from one equation into the other equation.

 

We know x = 4y - 3 so we plug in (4y - 3) into the second equation 

This becomes (4y - 3) - y = 6

4y - 3 -y = 6

then you can subtract the y from the 4y to get 3y

3y - 3 = 6 

then you have to add 3 to both sides of the = sign to make the equation balanced (and to get the variable alone on one side of the equation)

3y -3 + 3 = 6 + 3

simplify

3y = 9 

then divide both sides by 3 (always do the same thing on both sides of the = sign to make it balanced)

3/3y = 9/3

y = 3

Then plug in the solution for y into one of the two original equations to get the solution for x 

x - y = 6

x - 3 = 6

(add 3 on both sides of the equation)

x = 9

 

So the final answer is x = 9 and y = 3 and it's always best to plug in the numbers into both equations to check your work.