Nelson had 1/3 as many green marbles as blue marbles. If he bought another 36 green marbles, the ratio of the remaining number of green marbles to blue marbles is 2:5. How many marbles does he have altogether?
Nelson had 1/B as many green marbles as blue marbles.
G - B = 1/3 — 10
=> 3G - 3B = 1
If he bought another 36 green marbles, ratio of the remaining no : of green to blue marbles = 2:5
(G + 36)/B = 2/15 — (2)
5G + 180 = 2N.
5G - 2B = -180 — (2)
Solving (1) and (2)
(X2) 3G - 3B = 1
(X3) 5G -2B = -180
———————————————
-> 15G - 15B = 15
15G - 6B = - 540
———————-
9B = 555
B = 62
3G - 186 = 1
3G = 185
G = 62
Altogether there are = 124 marbles
X - green marbles at first
3X - blue marbles at first
(X+36)/3X = 2/5
X = 180 green marbles
180*3 = 540 blue marbles
180 + 540 = 720 marbles.
X = Y/3
X+36/Y = 2/5
Y = 540
X = 180
total 720 marbles initially
all together 720 + 36 = 756 finally
To solve this problem, let's break it down into steps:
Step 1: Let's assume the number of blue marbles Nelson initially had is represented by "x".
Step 2: According to the problem, Nelson initially had 1/3 as many green marbles as blue marbles. So the number of green marbles can be calculated as (1/3)x.
Step 3: If Nelson bought another 36 green marbles, the total number of green marbles will be (1/3)x + 36.
Step 4: After buying the additional marbles, the ratio of the remaining number of green marbles to blue marbles is 2:5. This means the remaining green marbles make up 2 parts out of a total of 2 + 5 = 7 parts.
Step 5: If the remaining green marbles make up 2 parts out of 7, then we can calculate the number of green marbles as (2/7) * [(1/3)x + 36].
Step 6: The remaining blue marbles will make up 5 parts out of 7. So the number of blue marbles can be calculated as (5/7) * x.
Step 7: Now that we have expressions for the number of green marbles and blue marbles, we can set up an equation to solve for x.
(2/7) * [(1/3)x + 36] = (5/7) * x
Step 8: Solving this equation will give us the value of x, which represents the initial number of blue marbles.
Step 9: Once we find the value of x, we can add the green and blue marbles to get the total number of marbles Nelson has.
I hope this breakdown helps to explain the steps involved in solving this problem!