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!
cost of one peppermint cookies = $ 0.6
cost of one cinnamon sugar cookies = $ 0.3
<h3><u>Solution:</u></h3>
Let "p" be the cost of one peppermint cookies
Let "c" be the cost of one cinnamon sugar cookies
<u><em>To find: cost of each cookie</em></u>
<h3><u><em>
On the first day, they sold 120 peppermint cookies and 30 cinnamon sugar cookies for a total of $81</em></u></h3>
We can frame a equation as:
120 peppermint cookies x cost of one peppermint cookies + 30 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81

120p + 30c = 81 --------- eqn 1
<h3><u><em>
The next day they made $60 by selling 70 peppermint cookies and 60 cinnamon sugar cookies</em></u></h3>
70 peppermint cookies x cost of one peppermint cookies + 60 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60

70p + 60c = 60 --------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "c"
Multiply eqn 1 by 2
240p + 60c = 162 --- eqn 3
Subtract eqn 2 from eqn 3
240p + 60c = 162
70p + 60c = 60
(-) -------------------------
170p = 102
<h3>p = 0.6</h3>
Substitute p = 0.6 in eqn 1
120p + 30c = 81
120(0.6) + 30c = 81
72 + 30c = 81
30c = 9
<h3>c = 0.3</h3>
<u><em>Summarizing the results:</em></u>
<em>cost of one peppermint cookies = $ 0.6</em>
<em>cost of one cinnamon sugar cookies = $ 0.3</em>
5(6)+5(7)=65 using distributive property