Question
Find two whole numbers his product is 147 and whose quotient is three
Answers
GPT-4o mini
Let the two whole numbers be \( x \) and \( y \).
According to the problem, we have two equations:
1. \( x \cdot y = 147 \) (their product)
2. \( \frac{x}{y} = 3 \) (their quotient)
From the second equation, we can express \( x \) in terms of \( y \):
\[
x = 3y
\]
Now, we can substitute this expression for \( x \) into the first equation:
\[
(3y) \cdot y = 147
\]
This simplifies to:
\[
3y^2 = 147
\]
Next, divide both sides by 3:
\[
y^2 = 49
\]
Taking the square root of both sides, we find:
\[
y = 7
\]
Now, substitute \( y \) back into the expression for \( x \):
\[
x = 3y = 3 \cdot 7 = 21
\]
Thus, the two whole numbers are \( x = 21 \) and \( y = 7 \).
To verify:
- Their product: \( 21 \cdot 7 = 147 \) (correct)
- Their quotient: \( \frac{21}{7} = 3 \) (correct)
Therefore, the two whole numbers are **21** and **7**.
According to the problem, we have two equations:
1. \( x \cdot y = 147 \) (their product)
2. \( \frac{x}{y} = 3 \) (their quotient)
From the second equation, we can express \( x \) in terms of \( y \):
\[
x = 3y
\]
Now, we can substitute this expression for \( x \) into the first equation:
\[
(3y) \cdot y = 147
\]
This simplifies to:
\[
3y^2 = 147
\]
Next, divide both sides by 3:
\[
y^2 = 49
\]
Taking the square root of both sides, we find:
\[
y = 7
\]
Now, substitute \( y \) back into the expression for \( x \):
\[
x = 3y = 3 \cdot 7 = 21
\]
Thus, the two whole numbers are \( x = 21 \) and \( y = 7 \).
To verify:
- Their product: \( 21 \cdot 7 = 147 \) (correct)
- Their quotient: \( \frac{21}{7} = 3 \) (correct)
Therefore, the two whole numbers are **21** and **7**.