Olivia is considering two phone plans. Plan A charges $20 per month, plus $0.05 per minute. Plan B charges $15 per month plus $0.10 per minute. How many minutes can Olivia talk so that both plans will cost the same amount? (Hint: Create an equation for each plan where y is the total cost and x is the minutes and then find the solution to the system of equations.)

Step-by-step explanation: Answer is 10

For this type of problem, we need to create a slope intercept equation for both.

Let's start by making one for plan a. We know that there is 20 dollars per month, this is the y intercept. Now, although it says per month which can change by x, the problem is mainly asking for minutes.

Remember, a slope intercept equation is

y=mx+b

M is the slope, and x is multiplied to the slope. The slope for an example can be used for this, adam eats 5 apples per day or x, how many apples can he eat in 5 days? We are wanting to know how many he can eat in 5 days, so we of course would multiply 5 by 5. This is basically a slope equation.

So, for plan a, we have y=0.05x+20 where x is minutes

For plan b, we should get

y=0.10x+15 where x is also minutes. The problem is asking use to find which value that we plug in will make both plan a and b correct. Basically, the value we find is x, so we solve for x by setting the two equations equal.

0.05x+20=.10x+15 Use inverse operations

20=.05x+15

5=.05x

x=10

We know if we plug in 10 for x, both would equal the same or 21 dollars.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

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