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3 years ago

8

The total price of four oranges and five pears is $32 while the total price of three oranges and two pears is $17. How much is a

pear?

2 answers:

Ket [755]3 years ago

8 0

Answer:

A pear is 3.4

Step-by-step explanation:

sweet-ann [11.9K]3 years ago

7 0

Answer: A pear cost $4.

Step-by-step explanation:

If the total price of four oranges and five pears is $32 then we could represent it by the equation 4x + 5y = 32 where x is cost of one orange and y is the cost of one pear.

The same way we could represent the second statement by the equation

3x + 2y = 17

We know have the two systems of equations:

4x + 5y = 32

3x + 2y = 17 Solve using the elimination method

Multiply the top equation by -3 and the down equation by 4 to eliminate x.

-3(4x + 5y) = -3(32) = -12x - 15y = -96

4(3x +2y) = 4(17) = 12x + 8y = 68

We now have the two new equations:

-12x -15y = -96 Add both equations

12x + 8y = 68

- 7y = -28

y= 4

Which means the cost of one pear is $4.

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For Commutative Property of Addition

Let us take a decimal number $2.14$ and a fraction $\frac{5}{20}$

Now, according to the Commutative property of Addition:

For any two numbers $a$ and $b$ :

$a+b = b+a$

So, for $2.14$ and $\frac{5}{20}$

Let us add

$2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}$

$=\frac{214}{100} + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100} + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39$

Also,

$\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}$

$= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Commutative Property of Addition is satisfied.

For Associated Property of Addition

Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

$a + (b+c) =(a+b) + c$

So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

Thus,

$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

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