Question

In the stamp collection below. The denominations have not been entered. Use the clues below to set up equations and determine the proper denominations.


Clue 1: The R stamps total 24 cents. R1 + R2 + R3 = 24

Clue 2: The R stamps with animals total 16 cents. R1 + R2 = 16
Combining this with Clue 1, we know R3 = 8

Clue 3: The stamps with animals total 20 cents. R1+ ___ + S2 = 20
Combining this with Clue 2, we know S2 = 4

Clue 4: The stamps with two animals total 13 cents. S2 + R2 = ___
Combining this with what we learned from Clue 3, we know R2 = ___

Clue 5: The two stamps with a person total 22 cents. ___ + T2 = 22
Combing this with what we learned from Clue 2, we know T2 = ___

Clue 6: The triangle stamps total 24 cents. T1 + ___ = 24
Combining this with what we learned from Clue 5, we know ___ = 10

Clue 7: The stamps with mechanical devices total 20 cents. T1 + R3 + S1 = ___
Combining this with what we learned from Clue 2 and Clue 6, we know S1 = ___

The S stamps total 11 cents. S1 + S2 + ___ = 11
Combining this with what we learned from Clue 3 and Clue 7, we know ___ = 5

Answer 1

1. R1 + R2 + R3 = 24

2. R1 + R2          =16       Subtract

                   R3=  8

3. R1 + R2 + S2 = 20

          16 + S2  = 20     Subtract 16 from both sides.

                   S2 =  4

4. S2 + R2 = 13

    4  + R2 = 13       Subtract 4 from both sides.

           R2 = 9

5. R3 + T2 = 22

     8 + T2 = 22

            T2 = 14

6. T1 + T2 = 24

   T1 + 14 = 24

   T1 = 10

7.  T1 + R3 + S1 = 20

    S1  + 8  + 10 = 20

    S1   + 18   =     20

    S1 = 2

S1 + S2 + S3 = 11

2 + 4 + S3 = 11

 S3 = 5

I don't see anything for R1 but R1 + R2 + R3 = 24

R1 + 9 + 8 = 24

R1 = 7

Summary

R1 = 8

R2 = 9

R3 = 8

S1 = 2

S2 = 4

S3 = 5

T1 = 10

T2 = 14                

Answer 2

Answer:

Clue 1: R1 + R2 + R3 = 24

Clue 2:  R1 + R2  =16  

Since, R1 + R2 + R3 = 24 (from clue 1)

R1 + R2 + R3 = 24

       16 + R3 = 24

Subtract both the sides by 16,

                 R3=  8

Clue 3:

We need to find the blank R1 + __ + S2 = 20 and S2 = 4

Since, R1 + R2 = 16 (from clue 2)

So, R1 + R2 + S2 = 20

             16 + S2  = 20    

Subtract 16 from both sides.

 16 + S2 - 16 = 20 -16

                       S2 =  4

So, R1 + R2 + S2 = 20

       

Clue 4:

We need to find the blank R2 = __

S2 + R2 = 13

Since, S2 = 4

 S2 + R2 = 13

  4 + R2 = 13

Subtract 4 from both sides.

           R2 = 9

So, R2 =  9

Clue 5:

We need to find the blank ___ + T2 = 22 and T2 = ___

R3 + T2 = 22

Since, R3 =8 ( from the Clue 2 )

   R3 + T2 = 22

     8 + T2 = 22

Subtract both the sides by 8,

          T2 = 14

So,  R3  + T2 = 22

Clue 6:

We need to find the blank T1 + ___ = 24 and  ___ = 10

Since, T1 + T2 = 24 ( from the Clue 5 )

         T1 + 14 = 24

Subtract both the sides by 14,

               T1 = 10

Clue 7:

We need to find the value of S1,

Given  T1 + R3 + S1 =20

Since, T1 = 10 and R3 = 8

10+ 8 + S1 = 20

     18 + S1 = 20

Subtract both the sides by 18,

  so,    S1  =  2

Combining this with what we learned from Clue 2 and Clue 6, we know

  S1  =  2  

Now, we need to find the blank,  S1 + S2 + ___ = 11

Combining this with what we learned from Clue 3 and Clue 7, we know

 ___ = 5

S1 + S2 + S3 = 11

  2 + 4 + S3 = 11

        6 + S3 = 11

Subtract both the sides by 6,

              S3 =  5  

For R1

Since, R1 + R2 + R3 = 24

R1 + 9 + 8 = 24

    R1 + 17 = 24

Subtract both the sides by 17,

            R1 = 7

Therefore,

R1 = 7

R2 = 9

R3 = 8

S1 = 2

S2 = 4

S3 = 5

T1 = 10

T2 = 14