Math

QuestionDetermine each friend's bus number (#4,#5,#8,#10,#12\# 4, \# 5, \# 8, \# 10, \# 12, or #15\# 15) using these clues: 1) Shaman's bus is 1/21/2 Ryeisha's, 2) Winston's is 2×2 \times Ellsworth's, 3) Ellsworth's is 1/31/3 Gina's, 4) Ami's is 3×3 \times Shaman's, 5) Ryeisha's is lower than Winston's.

Studdy Solution

STEP 1

Assumptions1. Each friend rides a different bus number #4, #5, #8, #10, #12, or #15. . Shaman's bus number is1/ of Ryeisha's bus number.
3. Winston's bus number is two times Ellsworth's bus number.
4. Ellsworth's bus number is1/3 of Gina's bus number.
5. Ami's bus number is three times Shaman's bus number.
6. Ryeisha rides a bus that has a lower number than Winston's.

STEP 2

Let's denote the bus numbers for each friend as follows Shaman (), Ryeisha (R), Winston (W), Ellsworth (), Gina (G), and Ami (A).

STEP 3

From the clues, we can form the following equations1. =1/2 * R2. W =2 *3. =1/3 * G. A =3 *5. R < W

STEP 4

We can substitute the equations into each other to form a single equation. From equation3, we know that =1/3 * G. Substituting this into equation2, we get W =2 * (1/3 * G) =2/3 * G.

STEP 5

From equation1, we know that =1/2 * R. Substituting this into equation4, we get A =3 * (1/2 * R) =3/2 * R.

STEP 6

Now we have the following equations1. =1/2 * R2. W =2/3 * G3. A =3/2 * R4. R < W

STEP 7

We can now start to assign bus numbers to the friends based on these equations and the constraints of the bus numbers.

STEP 8

Since R < W and W =2/3 * G, the only possible bus number for G is15. This is because15 is the only bus number that when multiplied by2/3 gives a result that is also a bus number (10). So, G =15.

STEP 9

Substitute G =15 into equation3 to find. =/3 * G =/3 *15 =5. So, =5.

STEP 10

Substitute =5 into equation2 to find W. W =2 * =2 *5 =10. So, W =10.

STEP 11

Since R < W and W =10, the only possible bus numbers for R are4,5, and8. But =5, so R cannot be5. Therefore, R can only be4 or8.

STEP 12

Substitute R =4 into equation to find. =/2 * R =/2 *4 =2. But2 is not a bus number, so R cannot be4. Therefore, R =8.

STEP 13

Substitute R =8 into equation to find. =/2 * R =/2 *8 =. So, =.

STEP 14

Substitute =4 into equation4 to find A. A =3 * =3 *4 =12. So, A =12.

STEP 15

Now we have assigned bus numbers to all the friends =4, R =8, W =10, =5, G =15, and A =12.
The solution is Shaman rides bus #4, Ryeisha rides bus #8, Winston rides bus #10, Ellsworth rides bus #5, Gina rides bus #15, and Ami rides bus #12.

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