Holly and Ross had a total of $60. After holly spent 1/4 of her money and Ross spent $5, the ratio of Holly's money became 1:2. How much more money did Ross have at the beginning?
Ross' total --- x
Holly's amount = 60-x
after spending:
Holly has (3/4)(60-x)
Ross has x-5
given:
Holly/Ross = 1/2
(3/4)(60-x) / (x-5) = 1/2
45 - (3/4)x / (x-5) = 1/2
90 - (3/2)x = x - 5
180 - 3x = 2x - 10
190 = 5x
x = 38
take over, using my definitions at the top
h+r = 60
(3/4 h)/(r-5) = 1/2
now just find h and r.
Not sure just what the question is asking. More than when he ended, or more than Holly?
Let's break down the problem step by step to find the answer.
Step 1: Figure out Holly's money after she spent 1/4 of it.
Since Holly's money was divided into a ratio of 1:2 after spending, let's assume she had x dollars initially. After spending 1/4 of her money, she would have (3/4)x dollars left.
Step 2: Figure out Ross's money after he spent $5.
If Holly had (3/4)x dollars left, which is equivalent to (3/4) of her original money, Ross would have (2/4)x dollars left because their ratio is 1:2. We know that Ross spent $5, so his original money would have been [(2/4)x + $5].
Step 3: Set up an equation.
We know that the total money they had initially was $60. Therefore, the sum of their money after spending is equal to $60.
[(3/4)x] + [(2/4)x + $5] = $60
Step 4: Solve the equation.
Combining like terms, we get: (5/4)x + $5 = $60
Subtracting $5 from both sides of the equation, we get: (5/4)x = $55
To isolate x, we multiply both sides of the equation by 4/5: x = ($55) * (4/5) = $44
Step 5: Find out how much more money Ross had at the beginning.
To find out how much more money Ross had at the beginning compared to Holly, we need to subtract Holly's money from Ross's money, which is [(2/4)x + $5] - $44.
Calculating this, we get [(2/4) * $44 + $5] - $44 = $22 +$5 - $44 = $27 - $44 = -$17
Therefore, Ross had $17 less money at the beginning.
So Ross had $17 less money at the beginning.