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vagabundo [1.1K]
3 years ago
6

Leia cuts congruent triangular patches with an area of 63 square centimeters from a rectangular piece of fabric that is 27 centi

meters long and 21 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?
Mathematics
1 answer:
m_a_m_a [10]3 years ago
6 0
<span>- The triangular patches have an area of 63 cm</span>² (A1= 63 cm²)<span>.
- The rectangular piece of fabric is 27 centimeters long and 21 centimeters wide. 

 1. Then, the first thing you must do is to calculate the area of the piece of fabric. The formula for the area of a rectangle is:

 A2=LxW
 
 L=27 centimeters (The lenght of the rectangle)
 W=21 centimeters (The width of the rectangle)

 2. When you substitute the values of L and W into the formula, you obtain:

 A2=(27 cm)(21 cm)
 A2=567 cm</span>²
<span>
 3. Then, let's calculate how many triangular patches she can cut from a rectangular piece of fabric:

 A2/A1= 567 cm</span>²/63 cm²= 9 triangular patches

 4. Finally, you can calculate how many triangular patches she can cut from 33 rectangular pieces of the fabric:

 (9 triangular patches)(33 pieces of fabric)=297 triangular patches
<span>
 How many of the patches can Leia cut from 33 pieces of the fabric?

 The answer is: 297 triangular patches</span>
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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.

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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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