Alice had 2/3 as many sweets as Jason. The ratio of Jason’s sweets to Bob’s sweets is 1:4. If Bob had 60 more sweets than Alice, find the total number of sweets that was shared among the three children at first.
A/J = 2/3 so 3 A = 2 J so 6 A = 4 J
J/B = 1/4 so 4 J = B = 6 A
and
B - A = 60
but we already know that B = 6 A
so 5 A = 60
A = 12 , (well there is hope)
then B= 6 A = 72
and J= B/4 = 18
12 + 72 + 18 = 102
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Check
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J/B = 4 ?
18 * 4 = 72 yes
A/J = 2/3 = ? 12/18 yes
B-A = 72-12 = 60 yes
Whew !
number of sweets for Jason --- x
number for Alice = (2/3)x or 2x/3
Jason : Bob = 1 : 4
x/Bob = 1/4
Bob = 4x
number for Bob = 4x
Bob - Alice = 60
4x - 2x/3 = 60
times 3
12x - 2x = 180
10x = 180
x = 18
Jason had 18, Alice had 12 and Bob had 72
for a total of 102
Check:
did Bob have 60 more than Alice ? YES
ratio of Jason : Bob = x : 4x = 1:4, as required
All looks good
To solve this problem, let's go step by step.
1. Let's start by finding the number of sweets Alice had in relation to Jason's number of sweets. We know that Alice had 2/3 as many sweets as Jason. So, let's assume that Jason had x number of sweets. Therefore, Alice had (2/3) * x sweets.
2. Next, let's find the number of sweets Bob had in relation to Jason's number of sweets. We are given that the ratio of Jason's sweets to Bob's sweets is 1:4. Therefore, Bob had (4/1) * x sweets.
3. We also know that Bob had 60 more sweets than Alice. So we can set up an equation: (4/1) * x = (2/3) * x + 60.
4. To solve the equation, let's eliminate the fractions by multiplying both sides by 3 to get: 12x = 2x + 180.
5. Now, let's simplify the equation by subtracting 2x from both sides: 12x - 2x = 180.
6. After simplification, we get: 10x = 180.
7. Now we can solve for x by dividing both sides by 10: x = 180/10.
8. This gives us x = 18, which represents the number of sweets Jason had.
9. Now we can find the number of sweets Alice had by substituting the value of x into the equation: Alice's sweets = (2/3) * 18 = 12.
10. Similarly, we can find the number of sweets Bob had by using the value of x: Bob's sweets = (4/1) * 18 = 72.
11. Finally, to find the total number of sweets shared among the three children, we add up their individual numbers of sweets: 18 + 12 + 72 = 102.
Therefore, at first, there were a total of 102 sweets shared among the three children.