Minah and Rohana had a total of $338. After Minah saved $49 more and Rohana spent half of her money, they both had the same about of money. How much did Minah have at first?
M + 49 = R/2
M+49 + R/2 = 338
Substitute R/2 for M+49 in the second equation and solve for R.
So whats the answer? Can you u give detail workings?
To solve this problem, we can break it down into smaller steps. Let's assign variables to the unknowns in the problem. Let M represent the amount of money Minah had at first, and let R represent the amount of money Rohana had at first.
We are given the following information:
1. Minah and Rohana had a total of $338. This can be expressed as: M + R = 338.
2. After Minah saved $49 more, her amount of money increased. So, Minah’s new amount of money can be represented as: M + 49.
3. After Rohana spent half of her money, her new amount of money can be represented as: R/2.
4. They both had the same amount of money after these changes. This can be expressed as: M + 49 = R/2.
Now, let's combine equations (1) and (4) to solve for the values of M and R.
From equation (1), we can rearrange it to get M = 338 - R.
Substituting this value into equation (4), we get:
338 - R + 49 = R/2.
Multiplying equation (4) by 2 to remove the fraction, we get:
676 - 2R + 98 = R.
Combining like terms, we have:
774 - R = R.
Re-arranging this equation, we get:
2R + R = 774.
Simplifying, we have:
3R = 774.
Dividing both sides by 3, we can solve for R:
R = 774/3 = 258.
Now that we have the value of R, we can substitute it back into equation (1) to solve for M:
M + 258 = 338.
Subtracting 258 from both sides, we get:
M = 338 - 258 = 80.
Therefore, Minah had $80 at first.