Jamin saved $15 each week, which was one-fourth of his weekly allowance. If x represents Jamin's weekly allowance, which three equations correctly represent this situation?
Understand the Problem
The question describes Jamin's savings and its relation to his weekly allowance. It asks us to identify three correct equations that represent the given information, where 'x' represents Jamin's weekly allowance. We know that $15 is one-fourth (1/4) of his total allowance.
Answer
$15 = \frac{1}{4}x$, $x = 60$, $30 = \frac{1}{2}x$
Answer for screen readers
The three correct equations are:
$15 = \frac{1}{4}x$
$x = 60$
$30 = \frac{1}{2}x$
Steps to Solve
- Expressing Jamin's savings in terms of his allowance
Jamin saves $15, which is one-fourth of his weekly allowance, $x$. We can express this relationship as an equation:
$15 = \frac{1}{4}x$
- Solving for the weekly allowance
To find Jamin's weekly allowance, we can multiply both sides of the equation by 4:
$4 \cdot 15 = 4 \cdot \frac{1}{4}x$
$60 = x$
So, Jamin's weekly allowance is $60.
- Creating equivalent equations
Now, let's generate some equivalent equations. From our initial equation:
$15 = \frac{1}{4}x$
Multiplying both sides by 4 gives:
$60 = x$ This is one possible equation
Multiplying both sides of the equation $15 = \frac{1}{4}x$ by 2 gives:
$30 = \frac{1}{2}x$ This is another possible equation
Starting from $60 = x$, we can divide both sides by 2:
$30 = \frac{1}{2}x$
We can also rearrange $15 = \frac{1}{4}x$ to $x = 4 \cdot 15$ or $x = 60$.
The three correct equations are:
$15 = \frac{1}{4}x$
$x = 60$
$30 = \frac{1}{2}x$
More Information
These equations all correctly represent the relationship between Jamin's savings and his weekly allowance. There are other possible correct equations as well. For example, any equation that simplifies to $x = 60$ is a correct equation.
Tips
A common mistake would be to incorrectly set up the initial equation. For example, writing $15 = 4x$ would mean that Jamin's savings are four times his allowance, instead of one-fourth. Another common mistake is not simplifying or manipulating the equation correctly to find equivalent forms.
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