need answer using bar model if possible

Question

David and Joseph have a total of 328 marbles. Mathew and David have 176 marbles. Joseph has 5 times as many marbles as Mathew.How many marbles does David have? need answer using bar model if possible

Answer 1

I cant draw a proper bar but I can give you an idea to solve using bar method.see David is commomn ,so I am going to put David first

 

 

 

[_David_] [_Mathew_]                           = 176

 

[_David_] [________Joseph_____________] = 328 

Its given that Joseph has 5 times as many marbles as Mathew.So we can divideJoseph's bar into 5 equal parts where each part represents Mathew's no.of marbels

 

[  David_][_Ma_][_Ma_][_Ma_][_Ma_][_Ma_] = 328  ;but David and Mathew has total 176 mrbl

{      178          }{ 4 times mathews marbels}

                                  328-176 =152

there fore Mathews has 152/4 = 38 marbels and so from first set of bars

 

 [_David_] [_Mathew_] = 176

 

David + 38  =  176

David =  176 -38  = 138

Answer 2

Let D = number of marbles David has

Let J = number of marbles Joseph has

Let M = number of marbles Mathew has

 

 

We can write equations using these variables to help us solve the problem.

 

D + J = 328            eq1

 

D + M = 176            eq2

 

J = 5M                    eq3

 

 

We have a system of equations.   Since we want to find how many marbles David has, we need to solve for the variable D.  However, we have 3 equations with 3 different variables.  So we need to use substitution and elimination methods.

 

 

First, we can substitute eq3 into eq1.  Let's get eq1 in terms of D and M.  In the end, we will have one less equation and one less variable to deal with.

 

D + 5M = 328          eq1

D + M = 176            eq2

 

 

We have only two equations as promised.

 

Next, we can multiply eq2 by 5.  Keep eq1 as it is.

 

D + 5M = 328                eq1

5D + 5M = 880               eq2

 

 

Subtract eq2 from eq1 to eliminate the M terms.

 

-4D = -552

 

 

Divide both sides of the equation by -4.

 

D = 138

 

 

David has 138 marbles.