If A is inversely proportional to B and A = 7 when B = 3, then what is the value of A when B = 2 1/3?
Understand the Problem
The question involves an inverse proportion between A and B. You're given that A = 7 when B = 3, and you need to find the value of A when B = 2 1/3 (which is 7/3). This involves setting up a proportionality equation and solving for A at the new value of B.
Answer
$A = 9$
Answer for screen readers
$A = 9$
Steps to Solve
- Write the inverse proportion equation
Since $A$ is inversely proportional to $B$, we write the relationship as: $A \propto \frac{1}{B}$, which implies $A = \frac{k}{B}$ for some constant $k$.
- Find the constant of proportionality k
Using the given condition, $A = 7$ when $B = 3$, we can find the constant $k$: $7 = \frac{k}{3}$ $k = 7 \times 3 = 21$
- Write the equation with the value of k
Now we have the equation $A = \frac{21}{B}$.
- Substitute the new value of B
We are looking for A when $B = 2\frac{1}{3} = \frac{7}{3}$. Substitute this value into the equation: $A = \frac{21}{\frac{7}{3}}$
- Solve for A
To solve for $A$, we divide 21 by $\frac{7}{3}$: $A = 21 \times \frac{3}{7} = \frac{21 \times 3}{7} = \frac{63}{7} = 9$
$A = 9$
More Information
The problem involves inverse proportionality, where an increase in one variable leads to a decrease in the other. The constant of proportionality helps to define the exact relationship between the two variables.
Tips
A common mistake is to misinterpret the inverse proportionality as a direct proportionality. Another common mistake is to incorrectly calculate the constant of proportionality $k$. When dividing a number by a fraction, remember to multiply by its reciprocal.
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