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?
I don't get it
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
Let's solve this step-by-step:
Let's assign variables to the given information:
Let the number of marbles David has be D.
Let the number of marbles Joseph has be J.
Let the number of marbles Mathew has be M.
From the first sentence, we know that David and Joseph have a total of 328 marbles:
D + J = 328 --------(equation 1)
From the second sentence, we know that Mathew and David have 176 marbles:
M + D = 176 --------(equation 2)
From the third sentence, we know that Joseph has 5 times as many marbles as Mathew:
J = 5M
Now, we can solve the system of equations using substitution to find the number of marbles David has.
Substitute the value of J from equation 3 into equation 1:
D + 5M = 328 --------(equation 4)
Substitute the value of M from equation 2 into equation 4:
D + 5(176 - D) = 328
Simplify the equation:
D + 880 - 5D = 328
-4D = 328 - 880
-4D = -552
Divide both sides by -4 to solve for D:
D = -552 / -4
D = 138
Therefore, David has 138 marbles.
To find out how many marbles David has, we'll need to break down the given information and solve step by step.
Let's assign variables to the unknown quantities:
- Let's represent the number of marbles David has as 'D'.
- Let's represent the number of marbles Joseph has as 'J'.
- Let's represent the number of marbles Mathew has as 'M'.
We are given the following information:
1. David and Joseph have a total of 328 marbles: D + J = 328.
2. Mathew and David have 176 marbles: M + D = 176.
3. Joseph has 5 times as many marbles as Mathew: J = 5M.
Now we can solve the system of equations to find the values of D, M, and J:
From equation 3, we can substitute the value of J in equation 1:
5M + D = 328. (Equation 4)
Now we have two equations:
M + D = 176. (Equation 2)
5M + D = 328. (Equation 4)
To solve this system of equations, we can subtract equation 2 from equation 4:
(5M + D) - (M + D) = 328 - 176,
4M = 152.
Dividing both sides of the equation by 4:
M = 152 / 4,
M = 38.
Substituting the value of M back into equation 3:
J = 5 * 38,
J = 190.
And substituting the values of M and J back into equation 1:
D + 190 = 328,
D = 328 - 190,
D = 138.
Therefore, David has 138 marbles.