there are 2 numbers whose sum is 50. Three times the first is 5 more than twice the second. What is the smaller number?

Question

It is a word problem that is confusing me and my friends and we dont understand it. Please help thanks.

Answer 1

Jonathan,

 

Just carefully follow the words and turn them into math expressions and relationships.  Since there are 2 numbers,

 

Let x = the first number

Let y = the second number

 

x + y = 50   since their sum is stated as 50.  BTW, at this point we don't know which is the bigger number.

3x = 5 + 2y  decode "is" as the = sign, and "5 more" as adding 5.

 

No solve these simply by addition by first rearranging the equations and multiplying the first by 2

2x + 2y = 100     doesn't change the equation since you multiplied both sides of the equal sign

3x -  2y = 5       to align the y terms so they drop out when both equations are added

5x = 105  and x = 105/5 = 21   then use the simple original equation (x + y = 50) to get y

3 + y = 50  so y = 50 - 21 = 29

 

Hence, x = 21 is the smaller number, and y = 29 are the 2 numbers that solve the problem