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vladimir2022 [97]
3 years ago
8

The cost depends upon the number of long distance minutes, m, Amy uses. Write the rule that describes Amy's monthly cost.

Mathematics
1 answer:
Yuri [45]3 years ago
3 0
Minutes(m)              Cost
0                                  20
10                                22
20                                24
50                                30

slope formula:
m = (y1 - y2) / (x1 - x2)
m = (20 - 22) / (0 - 10) = -2/-10 = 1/5 or 0.20

y = (1/5)(x) + 20

The rule that describes Amy's monthly cost is:
m = 1/5x + 20 or m = 0.20x + 20

Where x is the number of minutes spent on the call.

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Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table:           6, 12, 18, 24, ...

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First think, how would you work out the <u>7</u>th term in the <u>6</u>th times table?

You would do <u>6</u> times <u>7</u>.

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6n     (where n is the term you want to find out)

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Now lets compare the 6 times table to Andrew's pattern:

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Andrew's pattern:     3, 9, 15, 21,

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If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be:  6n - 3   (since it's the 6 times table but minus 3)

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We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = <u>117</u>    (remember, replace the n with 20)

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Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table:       5, 10, 15, 20

Ben's pattern:       3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

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<u>Now swap out the n for 20</u>  (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = <u>98</u>

_________________________________________

So Andrew's 20th term is <u>117</u>, and Ben's 20th term is <u>98</u>.

All we do now is subtract them to find the difference:

117 - 98 = <u>19</u>

- - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

Ben's 20th term is smaller by 19!

- - - - - - - - - - - - - - - - - - - - - - - - - -

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