Question

Parsons Bank offers two checking-account plans. The No Frills plan charges 45 cents per check whereas the SimpleChecking plan costs $4 per month plus 20 cents per check. For what number of checks per month will the SimpleChecking plan cost less?

Answer 1

The simple checking plan will be cheaper when there are more than 16 checks

Step-by-step explanation

Given that;

For the no frills plan

The charge per check is 45 cents

For the simple checking plan

The charge per month is $4

The charge per check is 20 cents

Follow the steps below to find the number of checks

Step 1; Set up an algebraic equation for the two plans

Plan A

Recall, 45 cents is equivalent to $0.45

Let x represents the number of check

Hence, the equation is written below

y = 0.45x -------- equation 1

Where y is the total cost

Plan B

Total cost = cost per month + cost per check x the number of checks

Therefore, we have

y = 0.20x + 4 ---------- equation 2

Step 2; Set up the inequality between the two plans

`\begin{gathered} \text{ Plan A cost > Plan B cost} \\ \text{ 0.45x > 0.20x + 4} \\ \text{ collect the like terms} \\ \text{ 0.45x - 0.20x > 4} \\ \text{ 0.25x > 4} \\ \text{ Divide both sides by 0.25} \\ \text{ x > }\frac{\text{ 4}}{\text{ 0.25}} \\ \text{ x > 16 } \end{gathered}`

The above calculations shows that x is greater than 161

So, if x = 20

Recall, 0.45x > 0.20x + 4

0.45 (20) > 0.20 (20) + 4

9 > 8

at x = 20, the simple checking plan is cheaper

Hence, the simple checking plan will be cheaper when there are more than 16 checks