david and joseph have a total of 328 marbles. Mathew and david have 176 marbles. joseph has 5 times as many as Mathew. how many marbles does david have?
math - Reiny, Sunday, March 31, 2013 at 3:10pm
d + j = 328
m+d = 176
j = 5m
put j = 5m into the first to find d
then put d into the second to find m
Now you know everybody's marbles
math - shohanur, Sunday, March 31, 2013 at 3:32pm
I don't get it
What part don't you get?
the put j=5m.... part
Joseph has 5 times as many as Mathew
To solve this problem, let's assign variables to the number of marbles each person has:
Let's say David has D marbles, Joseph has J marbles, Mathew has M marbles.
From the information given, we can form two equations:
Equation 1: D + J = 328 (David and Joseph have a total of 328 marbles)
Equation 2: M + D = 176 (Mathew and David have 176 marbles)
We also know that Joseph has 5 times as many marbles as Mathew, so we can write another equation:
Equation 3: J = 5M
We need to find the number of marbles David has (D).
To find the value of D, we can substitute equations (3) and (2) into equation (1).
Substituting equation (3) and (2) into equation (1), we have:
M + D + 5M = 328
Combining like terms, we get:
6M + D = 328
We can rewrite this equation as:
D = 328 - 6M
Now we have two equations:
Equation 2: M + D = 176
Equation 4: D = 328 - 6M
To solve these equations simultaneously, we can substitute equation (4) into equation (2):
M + (328 - 6M) = 176
Simplifying, we have:
328 - 5M = 176
Rearranging the equation:
-5M = 176 - 328
-5M = -152
Dividing both sides by -5, we get:
M = -152 / -5
M = 30.4
Since we cannot have a fractional number of marbles, we round M down to the nearest whole number:
M = 30
Now, we can substitute the value of M into equations (4) and (2) to find the values of D and J:
From equation (4):
D = 328 - 6M
D = 328 - 6(30)
D = 328 - 180
D = 148
David has 148 marbles.
From equation (2):
M + D = 176
30 + D = 176
D = 176 - 30
D = 146
Mathew has 30 marbles.
Therefore, David has 148 marbles.