Mr. Keskin and his wife have a cell phone plan that charges them $5 for 200 text messages per month for each of their phones. The Keskins are charged an additional $0.12 for each text message over their 200-text-message limit. Their carrier has offered them unlimited text messages for both lines for $30. What is the maximum number of text messages that they can send in a month to keep their current plan as the better deal? What is the minimum? Explain.
for m minutes,
current plan: 5.00 + .12(m-200)
proposed plan: 30.00
so, we want solve
5.00 + .12(m-200) < 30.00
m < 409
Please explain, i'm having trouble understanding.
do you understand the expressions for the current and proposed plans? Those are just symbols for the words that described the plans. Read the problem carefully, and wherever they give some information, write it down in numbers or symbols.
To solve for m, just do the regular steps for solving an equation:
5.00 + .12(m-200) < 30.00
5.00 + .12m - 24 < 30
.12m < 49
m < 408.3
Assuming charges are for whole messages, that means m < 409.
Ohh ok thank you! I understand now!
To determine the maximum and minimum number of text messages the Keskins can send in a month to keep their current plan as the better deal, we need to compare the costs of both options.
Under their current plan, the Keskins pay $5 for 200 text messages per month for each of their phones. For a combined total of 2 phones, they pay $5 x 2 = $10 for 200 text messages each.
For any text messages over their limit of 200, they are charged an additional $0.12 per text message. Let's assume they send x text messages over their limit. Therefore, the additional cost for exceeding the limit would be $0.12 * x.
Now, let's compare this cost to the cost of the unlimited text messages plan, which is $30.
To determine the maximum number of text messages, we need to find the point where the cost of the current plan (including overages) is equal to the cost of the unlimited plan.
For the current plan, the cost is $10 (for 200 messages each) + $0.12x (overage fee).
So, we have: $10 + $0.12x = $30
Subtracting $10 from both sides, we get: $0.12x = $20
Dividing both sides by $0.12, we find: x = 166.67
Since we cannot have a fraction of a text message, the maximum number of text messages the Keskins can send to keep their current plan as the better deal is 166 (rounded down to the nearest whole number).
To determine the minimum number of text messages, we need to find the point where the cost of the unlimited plan is less than the cost of the current plan (including overages).
For the current plan, the cost is $10 (for 200 messages each) + $0.12x (overage fee).
So, we have: $10 + $0.12x > $30
Subtracting $10 from both sides, we get: $0.12x > $20
Dividing both sides by $0.12, we find: x > 166.67
Since x represents the number of text messages and it cannot be a fraction, we round up to the nearest whole number. Therefore, the minimum number of text messages the Keskins can send to keep their current plan as the better deal is 167.
In summary, the maximum number of text messages the Keskins can send in a month to keep their current plan as the better deal is 166, while the minimum number is 167.