A bank offers two checking plans anywhere charge .15 cents a check; accucheck cost .77cents a month plus 8 cents per check.
For what number of checks will the accucheck plan cost less than anywhere check?
Less than 11 checks?
More than 11 checks?
11 checks?
11 or more checks?
11(.15) > .77m +11(.08)
Assuming one month:
1.65 = 1.65
< 11 checks
To determine the number of checks for which the accucheck plan will cost less than the anywhere check plan, we need to analyze the cost of both plans for different check quantities.
The cost of the anywhere check plan is calculated by multiplying the number of checks by $0.15. So, for x number of checks, the anywhere check plan would cost 0.15x.
The cost of the accucheck plan is a combination of a fixed monthly cost and a per-check cost. The fixed monthly cost is $0.77, and the per-check cost is $0.08. So, for x number of checks, the accucheck plan would cost 0.77 + 0.08x.
Now, let's compare the costs for different check quantities:
1. Less than 11 checks:
- Anywhere check plan cost: 0.15 * x
- Accucheck plan cost: 0.77 + 0.08x
To find the number of checks for which the accucheck plan cost is less than the anywhere check plan cost, we set the two costs equal to each other and solve for x:
0.15x = 0.77 + 0.08x
0.07x = 0.77
x = 0.77 / 0.07
x ≈ 11.0
Therefore, for less than 11 checks, the accucheck plan will cost less.
2. More than 11 checks:
- Anywhere check plan cost: 0.15 * x
- Accucheck plan cost: 0.77 + 0.08x
To find the number of checks for which the accucheck plan cost is less than the anywhere check plan cost, we set the two costs equal to each other and solve for x:
0.15x = 0.77 + 0.08x
0.07x = 0.77
x = 0.77 / 0.07
x ≈ 11.0
Therefore, for more than 11 checks, the anywhere check plan will cost less.
3. 11 checks:
- Anywhere check plan cost: 0.15 * 11 = $1.65
- Accucheck plan cost: 0.77 + 0.08 * 11 = $1.65
For 11 checks, both plans will cost the same.
4. 11 or more checks:
- Anywhere check plan cost: 0.15 * x
- Accucheck plan cost: 0.77 + 0.08x
To find the number of checks for which the accucheck plan cost is less than the anywhere check plan cost, we set the two costs equal to each other and solve for x:
0.15x = 0.77 + 0.08x
0.07x = 0.77
x = 0.77 / 0.07
x ≈ 11.0
Therefore, for 11 or more checks, the anywhere check plan will cost less.
In summary:
- For less than 11 checks, the accucheck plan is cheaper.
- For more than 11 checks, the anywhere check plan is cheaper.
- For exactly 11 checks, both plans cost the same.
- For 11 or more checks, the anywhere check plan is cheaper.