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White raven [17]
3 years ago
15

Solve:

Mathematics
1 answer:
Natalija [7]3 years ago
3 0
Answer: It took 18 Months for Michelle to collect 59 dolls.


Explanation:
First, let’s right an equation for this. Michelle started with 5 dolls in a bar collection (I have no clue what that is but i’ll roll with it), and each month she bought 3 more, so 5 dolls plus the 3 dolls per month equals 59 at some point.

5 dolls + 3 dolls per month = 59 dolls
OR
5 + 3m = 59

The point of this question is to find how many months (m) it took in order to get to 59 dolls and there’s multiple ways you can do this:

1) just plug in random numbers into m to see how long it takes to get to 59 [this option might take a while]

2) Try to isolate m (get every number out of the equation) to find out the value of m. [I’m most familiar with this way]

First, subtract 5 from 5 in the equation in order to get rid of it, since we’re trying to get all whole numbers out of the equation and only have m left. You subtract 5 from 59 since the equal sign is kind of like a mirrror, whatever you do to one side you have to do to the other. So, 5-5 is 0, and 59- is 54.

Now you’re left with 3m=54. In order to isolate the m, divide 3 by 3 to get rid of the 3, then divide 54 by 3, which is 18.

In order to check your work, plug 18 into m just to see if it works or not:

5+3m=59 —-> 5+ 3(18)= 59

3 times 18 is 54, plus 5 is 59. So, Mi hells took 18 months to collect her 59 dolls. Hope this helped!
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Answer:

see explanation

Step-by-step explanation:

both linear equations will have the form

y = mx + c ( m is the slope and c the y- intercept )

Chef Mate

c(n) = mn + c

calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table

m = \frac{18.5-14}{3-2} = \frac{4.5}{1} = 4.5 , then

c(n) = 4.5n + c ( n represents ounces )

To find c substitute any ordered pair from the table into c(n)

using (4, 23 )

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c(n) = 4.5n + 5 ← equation for Chef Mate

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

Similarly for Grocery Gourmet

g(n) = mn + c

using (2, 23 ) and (3, 27 ) to find m

m = \frac{27-23}{3-2} = \frac{4}{1} = 4 , then

g(n) = 4n + c

using (4, 31 ) to find c

31 = 16 + c ⇒ c = 31 - 16 = 15

g(n) = 4n + 15 ← equation for Grocery Gourmet

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

Equate the 2 equations to find when cost is the same

4.5n + 5 = 4n + 15 ( subtract 4n from both sides )

0.5n + 5 = 15 ( subtract 5 from both sides )

0.5n = 10 ( divide both sides by 0.5 )

n = 20

Then when n = 20

c(n) = 4.5(20) + 5 = 90 + 5 = 95

g(n) = 4(20) + 15 = 80 + 15 = 95

Both Chef Mate and Grocery Gourmet charge $95 for 20 ounces of extract

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