Answer :
Certainly! Let's go through the problem step-by-step to see if there is indeed only one possible pair of two-digit numbers that results when one is divided by the other and yields 0.15.
1. Understanding the problem: Elsa divides a two-digit number [tex]\( A \)[/tex] by another two-digit number [tex]\( B \)[/tex] and gets the result 0.15. This can be expressed as:
[tex]\[ \frac{A}{B} = 0.15 \][/tex]
which implies:
[tex]\[ A = 0.15 \times B \][/tex]
2. Defining the range: Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are both two-digit numbers, both must be between 10 and 99 inclusive.
3. Substituting values: For each two-digit number [tex]\( B \)[/tex], we will calculate [tex]\( A \)[/tex] as [tex]\( A = 0.15 \times B \)[/tex]. We need to check if [tex]\( A \)[/tex] is also a two-digit integer within the range from 10 to 99.
4. Finding the possible pairs:
- Suppose [tex]\( B = 80 \)[/tex]:
[tex]\[ A = 0.15 \times 80 = 12 \][/tex]
Since 12 is a two-digit number, this is a possible pair [tex]\((A, B) = (12, 80)\)[/tex].
5. Checking for other pairs:
- If [tex]\( B \)[/tex] takes values different from 80, we calculate [tex]\( 0.15 \times B \)[/tex]. If the result is not a two-digit integer between 10 and 99, we discard it.
- For [tex]\( B \)[/tex] values from 10 to 99, the only value that when multiplied by 0.15 results in a two-digit number is [tex]\( B = 80 \)[/tex].
6. Conclusion: After checking all possible values for [tex]\( B \)[/tex] in the range from 10 to 99, we find that the only pair [tex]\((A, B)\)[/tex] that satisfies [tex]\( \frac{A}{B} = 0.15 \)[/tex] with [tex]\( A \)[/tex] and [tex]\( B \)[/tex] being two-digit numbers is:
[tex]\[ (12, 80) \][/tex]
Therefore, Elsa is correct. There is only one possible pair of numbers that give the answer 0.15 when a two-digit number is divided by another two-digit number. This pair is [tex]\( (12, 80) \)[/tex].
1. Understanding the problem: Elsa divides a two-digit number [tex]\( A \)[/tex] by another two-digit number [tex]\( B \)[/tex] and gets the result 0.15. This can be expressed as:
[tex]\[ \frac{A}{B} = 0.15 \][/tex]
which implies:
[tex]\[ A = 0.15 \times B \][/tex]
2. Defining the range: Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are both two-digit numbers, both must be between 10 and 99 inclusive.
3. Substituting values: For each two-digit number [tex]\( B \)[/tex], we will calculate [tex]\( A \)[/tex] as [tex]\( A = 0.15 \times B \)[/tex]. We need to check if [tex]\( A \)[/tex] is also a two-digit integer within the range from 10 to 99.
4. Finding the possible pairs:
- Suppose [tex]\( B = 80 \)[/tex]:
[tex]\[ A = 0.15 \times 80 = 12 \][/tex]
Since 12 is a two-digit number, this is a possible pair [tex]\((A, B) = (12, 80)\)[/tex].
5. Checking for other pairs:
- If [tex]\( B \)[/tex] takes values different from 80, we calculate [tex]\( 0.15 \times B \)[/tex]. If the result is not a two-digit integer between 10 and 99, we discard it.
- For [tex]\( B \)[/tex] values from 10 to 99, the only value that when multiplied by 0.15 results in a two-digit number is [tex]\( B = 80 \)[/tex].
6. Conclusion: After checking all possible values for [tex]\( B \)[/tex] in the range from 10 to 99, we find that the only pair [tex]\((A, B)\)[/tex] that satisfies [tex]\( \frac{A}{B} = 0.15 \)[/tex] with [tex]\( A \)[/tex] and [tex]\( B \)[/tex] being two-digit numbers is:
[tex]\[ (12, 80) \][/tex]
Therefore, Elsa is correct. There is only one possible pair of numbers that give the answer 0.15 when a two-digit number is divided by another two-digit number. This pair is [tex]\( (12, 80) \)[/tex].