the ratio of Simone's pocket money to Fiona's pocket money was 2:3. After Fiona had received $5 from her mother, the ratio of Simone's pocket money to Fiona's pocket money became 4:7. how much pocket money did both of them have at first?
s = 2 f/3
s = 4 (f+5) /7
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2 f/3 = 4 f/7 + 20/7
2*21 f/3 = 4*21 f/7 + 20*21 /7
14 f = 12 f + 60
2 f = 60
so
f = 30
s = 2 f/3 = 20
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check
s/f = 20/30 = 2/3 yes
s/(f+5) = 20/35 = 4/7 yes, it worked
how about this approach:
Simone's money --- 2x
Fiona's money --- 3x
after mom's gift:
2x/(3x+5) = 4/7
14x = 12x + 20
2x = 20
x = 10
so Simone had 2x or $20
Fiona had 3x or $30
To solve this problem, let's first assign variables to represent Simone's and Fiona's initial pocket money.
Let's assume that Simone's initial pocket money is 2x dollars, and Fiona's initial pocket money is 3x dollars.
According to the given information, after Fiona receives $5 from her mother, the new ratio becomes 4:7. Therefore, the new amount of Simone's pocket money is 4x dollars, and Fiona's pocket money is 7x dollars.
Since Fiona receives $5, we can set up an equation to find the value of x:
3x + 5 = 7x
Now, let's solve the equation:
5 = 7x - 3x
5 = 4x
x = 5/4
Substituting the value of x back into the initial pocket money expressions:
Simone's initial pocket money = 2 * (5/4) = 10/4 = $2.50
Fiona's initial pocket money = 3 * (5/4) = 15/4 = $3.75
Therefore, Simone initially had $2.50, and Fiona initially had $3.75 as their pocket money.