What number am I?
I am a multiple of 3
I am also a multiple of 7
My units digit is half my tens digit
21
21
thought you said you don't give people answers Ms. Sue
I'm a professional teacher and I use my experience and my judgement to make that decision.
To find the number that satisfies all the given conditions, we can use a step-by-step approach:
Step 1: Start with the fact that the number is a multiple of 3. All multiples of 3 can be expressed as 3 times some integer. Let's represent this integer as "x," so the number can be written as 3x.
Step 2: Next, take into consideration that the number is also a multiple of 7. Similarly, all multiples of 7 can be expressed as 7 times some integer. Let's represent this integer as "y," so the number can now be written as 3x = 7y.
Step 3: We are also given that the units digit is half the tens digit. Let's represent the tens digit as "t" and the units digit as "u," so that the number can be expressed as 10t + u. According to the condition, u = (1/2) * t.
Step 4: Apply the condition that the number is a multiple of 3 to the expression 10t + u = 3x. A number is divisible by 3 if the sum of its digits is divisible by 3. So, we can rewrite the equation as 1 + t + u = 3x.
Step 5: Substitute u = (1/2) * t into the equation from step 4. This gives us 1 + t + (1/2) * t = 3x.
Step 6: Simplify the equation from step 5 by combining like terms. It becomes 1.5t + 1 = 3x.
Step 7: Rearrange the equation from step 6 by multiplying both sides by 2/3 to get t alone. This gives us t = (2/3)(3x-1).
Step 8: Based on the given conditions, t must be a single-digit number since it represents the tens digit. Therefore, the possible values for t are 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Step 9: Substitute the values of t into the expression 10t + u to get the number. For each value of t, calculate u = (1/2) * t and substitute it into 10t + u.
By following these steps, you can determine which number satisfies all the given conditions.