Sure, let's carefully break down the solution to the problem.
(a) To form an equation that can represent the situation, we need to decide which numbers to plug into appropriate places in one of the equations given.
Let [tex]\( x \)[/tex] represent the number of t-shirts sold.
The equation that fits the scenario can be written considering that we must relate [tex]\( x \)[/tex] to the given numbers 83, 5, and 22. The appropriate equation form would be:
[tex]\[ 5x - 22 = 83 \][/tex]
(b) Now we will solve this equation to find the value of [tex]\( x \)[/tex]:
[tex]\[ 5x - 22 = 83 \][/tex]
First, isolate [tex]\( 5x \)[/tex] by adding 22 to both sides of the equation:
[tex]\[ 5x = 83 + 22 \][/tex]
[tex]\[ 5x = 105 \][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ x = \frac{105}{5} \][/tex]
[tex]\[ x = 21 \][/tex]
So, the number of t-shirts sold is:
[tex]\[ x = 21 \][/tex]
Therefore, she sold 21 t-shirts.
