solve this word problem. a bank offers two accounts. Their local plan charges $7 monthly service fee plus $3 for each transaction. There Anywhere plan charges $23 monthly service fee plus $1.75 per transaction. For what number of transactions per month will the Anywhere plan cost less?
we want
23 + 1.75x < 7 + 3x
Now just solve for x
wank
To solve this word problem, we need to find the number of transactions per month where the Anywhere plan will cost less than the Local plan.
Let's denote the number of transactions per month as "x".
For the Local plan, the monthly cost can be calculated as: $7 (monthly service fee) + $3 (per transaction fee) * x (number of transactions).
So, the equation for the monthly cost of the Local plan is: Cost_L = 7 + 3x.
For the Anywhere plan, the monthly cost can be calculated as: $23 (monthly service fee) + $1.75 (per transaction fee) * x (number of transactions).
So, the equation for the monthly cost of the Anywhere plan is: Cost_A = 23 + 1.75x.
We want to find the number of transactions, "x", where the Anywhere plan cost is less than the Local plan cost.
Therefore, we need to solve the inequality: Cost_A < Cost_L.
Substituting the equations, we have:
23 + 1.75x < 7 + 3x.
To simplify the inequality, let's move all terms involving "x" to one side:
1.75x - 3x < 7 - 23.
This becomes:
-1.25x < -16.
Next, divide both sides of the inequality by -1.25 to isolate "x":
x > -16 / -1.25.
x > 12.8.
Since the number of transactions must be a whole number, we can round up to the nearest whole number to get the minimum number of transactions required where the Anywhere plan costs less.
Therefore, the Anywhere plan will cost less than the Local plan when the number of transactions per month is 13 or more.