Question

A popular cell phone family plan provides 1500 minutes. It charges 89.99/month for the first 2 lines and 9.99 for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.

100

likes
501 views

Answer to a math question A popular cell phone family plan provides 1500 minutes. It charges 89.99/month for the first 2 lines and 9.99 for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.

Expert avatar
Seamus
4.9
98 Answers
To solve this problem, let's first set up an inequality to represent the situation.

Let x be the number of cell phone lines the family can afford.

The monthly cost for the first 2 lines is $89.99 each, so the total cost for these lines is $89.99 + $89.99 = $179.98.

For each additional line after the first 2, the cost is $9.99. Since there are x - 2 additional lines after the first 2, the cost for these lines is 9.99 * (x - 2).

In addition, the family has to pay $30.00/month for unlimited text messages for all phone lines and $10.00/month for Internet per phone line.

So the total monthly cost, including the text messages and Internet, can be expressed as:

179.98 + 9.99 * (x - 2) + 30.00 + 10.00x ≤ 200.00

Simplifying the inequality, we have:

179.98 + 9.99x - 19.98 + 30 + 10.00x ≤ 200.00
-9.99x + 9.99x + 19.99x ≤ 200.00 - 179.98 - 30 - 19.99
39.98x ≤ 190.03

Now, we can solve for x:

x ≤ \dfrac{190.03}{39.98}
x ≤ 4.7529

Since we cannot have a fractional number of cell phone lines, the family can afford a maximum of 4 lines.

Answer: The family can afford a maximum of 4 cell phone lines.

Frequently asked questions (FAQs)
How many diagonals does a dodecagon have?
+
What is the surface area of a rectangular prism with length 5 cm, width 9 cm, and height 12 cm?
+
What is the value of log(base 3)337 in its simplest form?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
Add. 7/w²+18w+81 + 1/w²-81
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
3(4x-1)-2(x+3)=7(x-1)+2
Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
9b^2-6b-5
(2b) to the 1/4th power. Write the expression in radical form.
If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
A recurring sequence is one where elements repeat after completing one standard. If the sequence AB8C14D96AB8C1... is recurring its twentieth term is equal to: (A) B. (B) 8. (C) A. (D) 6. (E) D.
Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block. A. What is the acceleration of the blocks? B. What is the force of the 4.3-kg block on the 5.4 -kg block? C. What is the force of the 5.4 -kg block on the 4.3 -kg block?
A company receives sales in $20 per book and $18 per calculator. The per unit cost to manufacture each book and calculator are $5 and 4$ respectively. The monthly (30 day) cost must not exceed $27000 per month. If the manufacturing equipment used by the company takes five minutes to produce a book and 15 minutes to produce a calculator, how many books and calculators should the company produce to maximise profit? Please solve graphically and
In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
viii. An ac circuit with a 80 μF capacitor in series with a coil of resistance 16Ω and inductance 160mH is connected to a 100V, 100 Hz supply is shown below. Calculate 7. the inductive reactance 8. the capacitive reactance 9. the circuit impedance and V-I phase angle θ 10. the circuit current I 11. the phasor voltages VR, VL, VC and VS 12. the resonance circuit frequency Also construct a fully labeled and appropriately ‘scaled’ voltage phasor diagram.
In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1
Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.
How many moles are there in 235 grams of potassium thiosulfate pentahydrate? K2S2O3*5(H2O)
Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?