Directions: Using the digits 0 to 9 as many times as you want, fill in the boxes to create a correct number sentence.

### Hint

This problem could also be stated, “x is 50% of y and 75% of z”. Start by considering x is 50% of y. What numbers satisfy this relationship? What do you notice about these numbers. Now consider that x is also 75% of z. What do you know about numbers that must be 1/2 of a number and also 3/4 of a number?

### Answer

There are 17 different solutions to this question. A few of these are: 6 is 50% of 12 and 75% of 8

15 is 50% of 30 and 75% of 20

21 is 50% of 42 and 75% of 28

42 is 50% of 84 and 75% of 56

There are 4 different solutions to the challenge question:

18 is 50% of 36 and 75% of 24

27 is 50% of 54 and 75% of 36

36 is 50% of 72 and 75% of 48

39 is 50% of 78 and 75% of 52

15 is 50% of 30 and 75% of 20

21 is 50% of 42 and 75% of 28

42 is 50% of 84 and 75% of 56

There are 4 different solutions to the challenge question:

18 is 50% of 36 and 75% of 24

27 is 50% of 54 and 75% of 36

36 is 50% of 72 and 75% of 48

39 is 50% of 78 and 75% of 52

Extension/Challenge: Try to create this number sentence using each digit no more than once.

Source: Erick Lee

30 50% 60 and 75% 40

06 is 50% of 12 and is 75% of 8

03 is 50% of 06 and is 75% of 4.

09 is 50% of 18 and 75% of 12

12 is 50% 24 and is 75% of 16

15 is 50% of 30 and 75% of 20

18 is 50% of 36 and 75% of 24

21 is 50% of 42 and 75% of 28

24 is 50% of 48 and 75% of 32

27 is 50% of 54 and 75% of 36

30 is 50% of 60 and 75% of 40

33 is 50% of 66 and is 75% 44

36 is 50% of 72 and is 75% of 48

39 is 50% of 78 and is 75% of 56

42 is 50% of 84 and is 75% of 60

45 is 50% of 90 and is 75% of 64

48 is 50% of 96 and is 75% of 68

30 50% 60 and 75% 40

21 is 50% of 42 and 75% of 28

15 is 50% of 30 and 75% of 20

36 is 50% of 72 and 75% of 48

03 is 50% of 06 and 75% of 04.

06 is 50% of 12 and 75% of 08

Are there only 16 solutions?

There are 17 solutions.

okay here me out here…..

00 is 50% of 00 and 75% of 00.

😛

42 is 50% and 84 and 75% of 60