The equations are as follows where x represents the number of minutes the cell phone is used.
For plan one: Total cost = $20 + $0.15x
For plan two: Total cost = $35 + $0.10x
For both the costs to be the same, we need to use the cell phone for
300 minutes.
Equations are relations showing the value of one quantity related to another quantity when it can change. The changing value is the variable.
We are informed that one cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used.
We are asked to write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.
Let the number of minutes the cell phone is used be x minutes.
Now we solve for equations for both plans in the following way:-
Plan one:
Charges $20 per month plus $0.15 per minute used.
When the use is for x minutes, the additional charge = $0.15*x = $0.15x
∴ Total cost = Fixed cost + Additional cost
or, Total cost = $20 + $0.15x.
Plan two:
Charges $35 per month plus $0.10 per minute used.
When the use is for x minutes, the additional charge = $0.10*x = $0.10x
∴ Total cost = Fixed cost + Additional cost
or, Total cost = $35 + $0.10x.
We are asked to find the number of minutes used so that the costs in both the plans are equal. To find this we equate the equation of total costs in both the cases to get:
$20 + $0.15x = $35 + $0.10x.
Subtracting ($20 + $0.10x) from both sides of the equation, we get
$20 + $0.15x - ($20 + $0.10x) = $35 + $0.10x - ($20 + $0.10x).
or, $20 + $0.15x - $20 - $0.10x = $35 + $0.10x - $20 - $0.10x.
or, $0.05x = $15
Dividing both sides of the equation by $0.05, we get
$0.05x/$0.05 = $10/$0.05
or, x = 300.
∴ We must talk for 300 minutes for both the plans to cost the same to us.
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What is the minimum whole number of packages Renna needs to remove from the elevator to meet the mass requirement?
Answer:
Part A. 37.4p ≥ 170
Part B. p ≥ 5 (rounding to the next whole)
Renna needs to remove at least 5 packages from the elevator to meet the mass requirement.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Mass limit for the elevator = 450 kg
Renna and her load of packages mass = 620 kg
Each package mass = 37.4 kg
2. Write an inequality to determine the number of packages, p, Renna could remove from the elevator to meet the mass requirement.
Number of packages * Each package mass ≥ Renna and her load of packages mass - Mass limit for the elevator
Replacing with the values and variables we know:
p * 37.4 ≥ 620 - 450
37.4p ≥ 170
3. What is the minimum whole number of packages Renna needs to remove from the elevator to meet the mass requirement?
Solving for p in the equation above, we have:
37.4p ≥ 170
p ≥ 170/37.4
p ≥ 4.55
p ≥ 5 (rounding to the next whole)