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notsponge [240]
3 years ago
8

Mr hopper did the rest need help

Mathematics
2 answers:
Contact [7]3 years ago
7 0

Let g = graph paper and r = ruler

1st equation: 5g + 30r = 40

2nd equation: 12g + 20r = 44

Multiply the 2nd equation by -1.5 to cancel out the r's

2nd equation: 12g + 20r = 44 x -1.5 = -18g - 30r = -66

Now add the 1st equation to that:

-18g + 5g = -13g

30r -30r = 0

40 -66 = -26

The new equation becomes -13g = -26

Divide both sides by -13

g = -26 / -13

g = 2

This means each pack of graph paper cost $2.

Now replace g with 2 in the first equation to solve for the cost of a rule:

5(2) + 30r = 40

Simplify:

10 + 30r = 40

Subtract 10 from each side:

30r = 30

Divide both sides by 30:

r = 30 / 30

r = 1

Each rule cost $1.

Shkiper50 [21]3 years ago
5 0
.-..........................
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3 years ago
Phoebe, Andy and Polly share £270.
Stella [2.4K]
*Given
Money of Phoebe            - 3 times as much as Andy
Money of Andy                - 2 times as much as Polly
Total money of Phoebe,  - <span>£270
</span>    Andy and Polly

*Solution

Let
B - Phoebe's money
A - Andy's money
L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total <span>£270. Thus, 
</span>
                  B + A + L  = <span>£270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as
  
                  B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                  A = 2L</span>                           (EQUATION 2)
<span>
4. This means that Phoebe has ____ as much money as Polly, 

                 B = 3A
                 B = 3 x (2L)
                 B = 6L                            </span>(EQUATION 3)<span>

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only. 

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes, 

                  6L + 2L + L = </span><span>£270
</span>                                9L = <span>£270
</span>                                  L = <span>£30

So, Polly has </span><span>£30. 

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively. 
</span>
                  A = 2L                           
                  A = 2(£30)
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Andy has £60

                  B = 6L                         
                  B = 6(£30)
                  B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
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Answer:

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