David and Joseph have a total of 328 marbles. Matthew and David have 176 marbles. Joseph has 5 times as many marbles as Matthew. How many marbles does David have?

Solve system: D + J = 328 M + D = 176 J = 5M Hint: if you substitute 5M into J of the first equation then you get a system of two equations with two unknowns M and D which you can easily solve: D + 5M = 328 D + M = 176

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altavistard altavistard · Answer 2 · 2017-11-13T01:36:38+01:00

d: count of David's marbles
j: count of Joe's marbles
m: count of Matt's marbles

Then d + j = 328 => d + 5m = 328
and m+d = 176 => -d - m = -176
and j = 5m These two equations combine to produce
4m = 152. Thus, m = 152/4 = 38.

If m = 38, then j = 5(38) = 190. Thus, d = 328 - j, or 328 - 190, or 138.

Dave has 138 marbles, Matthew has 38, and Joe has 190.

d + j = 328
-(d + m = 176)
----------------------
j -m = 152. But m = j/5, so j - j/5 = 152. Then 4j/5 = 152, or

(5/4)(4j/5) = (5/4)(152) = 190. j = 190. Since d + j = 328, d = 138.

David has 138 marbles. Joe has 5 times as Matt or 120. m has 96 marbles.