Minah and rohana had a total of $338 at first. After minah’s mother gave her another $49 and rohana spent half of her money, they both had the same amount of money. How much did Minah have at first?
m+r = 338
m+49 = r/2
m+49 = (338-m)/2
m = 80
check:
Minah had $80 and Rohana had $258
Later,
Minah had 80+49 = $129
and
Rohana had 258/2 = $129
Well, it seems like Minah's mother gave her some extra cash to even things out, but we're not quite sure of the initial amount Minah had. Let's put on our detective hats and solve this mystery together!
Let's assume Minah had x dollars at first. So, after Minah's mother gave her $49, she would have had x + 49 dollars.
Now, Rohana spent half of her money, which means she had (x + 49)/2 dollars left.
We're told that after these transactions, Minah and Rohana had the same amount of money. So, according to our calculation, x + 49 = (x + 49)/2.
To solve this equation, we can multiply both sides by 2 to get rid of the fraction: 2(x + 49) = x + 49.
Expanding the equation gives us 2x + 98 = x + 49.
Now, if we subtract x from both sides and subtract 49 from both sides, we get x = 49.
So, Minah had $49 at first! Case solved, mystery solved!
Let's solve this step-by-step.
Let's assume Minah had $x at first.
Rohana had $338 - $x at first.
After Minah's mother gave her $49, Minah had $x + $49.
After Rohana spent half of her money, Rohana had ($338 - $x)/2.
They both had the same amount of money, so we can set up the equation:
$x + $49 = ($338 - $x)/2
Multiplying both sides by 2:
2($x + $49) = $338 - $x
Expanding:
$2x + $98 = $338 - $x
Combining like terms:
$3x + $98 = $338
Subtracting $98 from both sides:
$3x = $240
Dividing both sides by $3:
x = $80
Therefore, Minah had $80 at first.
To solve this problem, we can set up equations based on the information given:
Let's assume that Minah had x dollars at first, and Rohana had y dollars at first.
1. The total amount of money they had at first is $338:
x + y = 338
2. Minah's mother gave her an additional $49, which means that Minah now has x + 49 dollars.
3. Rohana spent half of her money, which means she has (1/2)y dollars remaining.
4. After these changes, they both had the same amount of money:
x + 49 = (1/2)y
Now, we can solve this system of equations to find the value of x, which represents the amount Minah had at first.
Substitute x + 49 from equation 2 into equation 4:
x + 49 = (1/2)y
Rearrange equation 1 to solve for y:
y = 338 - x
Substitute (338 - x) for y in equation 4:
x + 49 = (1/2)(338 - x)
Now we can solve this equation for x:
Multiply both sides by 2:
2(x + 49) = 338 - x
Distribute:
2x + 98 = 338 - x
Combine like terms:
2x + x = 338 - 98
3x = 240
Divide both sides by 3:
x = 80
Therefore, Minah had $80 at first.