Bob, jean, and Paul have a total of 5590 stickers. Paul has twice as many stickers as Bob. Bob has 3 times as many stickers as Jean. How many stickers does each one have
Jean --- x
Bob ---- 3x
Paul ---- 6x
x+3x+6x = 5590
take over
5590
Let's assign variables to represent the number of stickers each person has.
Let's say Bob has x stickers.
Jean has 1/3 * x stickers.
Paul has 2x stickers.
According to the given information, the total number of stickers is 5590.
So we can write the equation: x + 1/3 * x + 2x = 5590.
Combining like terms, we get: (1 + 1/3 + 2) * x = 5590.
Calculating the sum inside the parentheses, we get: (4/3) * x = 5590.
To solve for x, we divide both sides of the equation by 4/3: x = 5590 / (4/3).
Simplifying the right side of the equation, we get: x = 5590 * (3/4).
Calculating the right side of the equation, we get: x = 4192.5.
So, Bob has approximately 4192.5 stickers.
To find Jean's number of stickers, we multiply Bob's number by 1/3: 4192.5 * 1/3 = 1397.5.
So, Jean has approximately 1397.5 stickers.
To find Paul's number of stickers, we multiply Bob's number by 2: 4192.5 * 2 = 8385.
So, Paul has approximately 8385 stickers.
Therefore, Bob has approximately 4192.5 stickers, Jean has approximately 1397.5 stickers, and Paul has approximately 8385 stickers.
To solve this problem, we can set up a system of equations. Let's denote the number of stickers Bob has as B, the number Jean has as J, and the number Paul has as P.
We are given three pieces of information in the problem:
1. Paul has twice as many stickers as Bob: P = 2B.
2. Bob has three times as many stickers as Jean: B = 3J.
3. The total number of stickers they have is 5590: B + J + P = 5590.
We can now solve this system of equations to find the values of B, J, and P.
Using equation 2, we can substitute the value of B in equation 1: 3J = 2B.
Next, let's substitute equation 2 into equation 3 to eliminate B: 3J + J + 2B = 5590.
Substituting equation 1 into equation 3 gives us: 3J + J + 2(3J) = 5590.
Expanding the expression gives us: 3J + J + 6J = 5590.
Combining like terms: 10J = 5590.
Divide both sides of the equation by 10: J = 559.
Now we know that Jean has 559 stickers.
Using equation 2, we substitute the value of J: B = 3(559) = 1677.
Bob has 1677 stickers.
Lastly, using equation 1, we substitute the value of B: P = 2(1677) = 3354.
Paul has 3354 stickers.
In conclusion, Bob has 1677 stickers, Jean has 559 stickers, and Paul has 3354 stickers.