SOLUTION: Jake, Mandy and Ann had 360 sweets in the ratio 4:3:5 respectively. Jake gave 1/3 of his sweet to Mandy and Ann gave 40% of her sweets to Jake. What was the ratio of Jake's sweet t
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-> SOLUTION: Jake, Mandy and Ann had 360 sweets in the ratio 4:3:5 respectively. Jake gave 1/3 of his sweet to Mandy and Ann gave 40% of her sweets to Jake. What was the ratio of Jake's sweet t
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Question 1197783: Jake, Mandy and Ann had 360 sweets in the ratio 4:3:5 respectively. Jake gave 1/3 of his sweet to Mandy and Ann gave 40% of her sweets to Jake. What was the ratio of Jake's sweet to Ann's sweets in the end? Found 2 solutions by josgarithmetic, math_tutor2020:Answer by josgarithmetic(39618) (Show Source):
Jake has 4x pieces, Mandy has 3x, and Ann has 5x.
Their counts total to 360.
4x+3x+5x = 360
12x = 360
x = 360/12
x = 30
Then we can find the following:
Jake = 4x = 4*30 = 120
Mandy = 3x = 3*30 = 90
Ann = 5x = 5*30 = 150
Check so far:
jake + mandy + ann = 120+90+150 = 210+150 = 360
This confirms we did things correctly.
Jake has 120 sweets
He gives 1/3 of it to Mandy
1/3 of 120 = (1/3)*120 = 40
He gives 40 pieces to Mandy
Jake: 120 to 120-40 = 80
Mandy: 90 to 90+40 = 130
Ann has 150 pieces. She gives 40% to Jake.
40% of 150 = 0.40*150 = 60
She gives him 60 pieces.
Jake: 80+60 = 140
Ann: 150-60 = 90
We have these counts at this point
Jake = 140
Mandy = 130
Ann = 90
Add those three values up and you should get 360 as a checksum.
We haven't introduced new pieces of candy, nor taken away any from the entire group. All that has been done is the candy is shifted around.
The ratio of Jake's candy count to Ann's count is
Jake: Ann
140:90
14:9
I divided both parts by the GCF 10 to reduce the ratio
Answer is 14:9
Edit: The tutor @josgarithmetic has made a typo in simplifying . The simplified result is NOT . Instead, it should be
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