The sum of two numbers is 100. Twice the first number is equal to 5 times the sum of the second number and 5

Question

I cant figure this question out. Can someone specifically describe how to solve it. Help is greatly appreciated

Answer 1

The tough part of word (story) problems is usually the translation.

Assign F=first number and S=second number.
“The sum of two numbers is 100”     means       F + S = 100
“Twice the first number is equal to 5 times the sum of the second number and 5”     means
      2       *    F                      =          5     *       (                 S               +   5  )

Let’s use elimination, so multiply the first equation by 2 so we can subtract the F:
        2F + 2S = 200           (2 * first equation)
        2F          = 5(S+5)      (second equation)
       ----------------------
               2S  = 200 - 5S -25        (subtract equations)
                7S =  175              (collect S terms)
                  S = 25              (divide both sides by 7)

Put value of S into first equation:
                  F + 25 = 100
                  F = 75

Checking (very important):
      Is 75 + 25 = 100   ?   yes.
      Is  2*75 = 5*(25+5)   ?
           150   = 5*30    ?    yes,

Answer 2

X + y = 100  converting the words in algebraic expression

2x = 5(y+5)

x+y =100

2x=5y+25          resolving internal operations

 

X = 100-y           isolating one of the variables, the x

2x =5y+25

 

X=100-y          continuing isolating x

x=5y/2 + 25/2

 

100-y = 5y/2 + 25/2   comparison of two algebraic expressions with only one variable

 

-y -5y/2 = 25/2 - 100  isolating the variable

 

-2y -5y = 25 - 200    Simplify the denominator in both sides

 

-7y = -175    resolving internal operations like terms

 

y= -175/-7 continuing isolating  y

 

y = 25    resolving internal operations

 

x + y = 100  with the value found for the variable y substitute is in the first equation

x + 25 = 100

x = 100 - 25  isolate the other variable and resolve the internal problems to find the value of the other variable

 

x = 75

 

the two numbers are x=75 and y=25

thanks

Answer 3

let the first no be x and the second be y

 

so x+y=100    .let this be equation 1

 

now it is given that twice of first = 5 times(y+5)

ie 2x= 5(y+5)   let this be equation 2

 

 now we want to solve these 2 equations to get the values of x and y

 

multiply eqn 1 by 2 on both sides to get 2x +2y= 200 

plug in the value of 2x from eqn 2

so we get

 

 5y +25 +2y= 200

 

ie 7y =175

ie y= 175/7

y= 25 

 

hence x is 100-25

xis 75