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Cloud [144]
3 years ago
15

Samantha wants to use her savings of 1150 to buy shirts and watches for her family. The total price of the shirt she bought was

$84. The watches cost $99 each what is the maximum number of watches that Samantha come by with her savings?
Mathematics
1 answer:
ioda3 years ago
8 0

<u>Answer-</u>

<em>The maximum number of watches that Samantha come by with her savings is </em><em>10</em><em>.</em>

<u>Solution-</u>

The amount of money Samantha has in her savings account = $1150

She wants to buy shirts and watches.

Cost of one shirt = $84

Cost of each watch = $99

Let she can buy maximum of x watches, so the net price of the watches is $99x.

Then,

\Rightarrow 99x+84=1150\\\\\Rightarrow 99x=1150-84\\\\\Rightarrow 99x=1066\\\\\Rightarrow x=\dfrac{1066}{99}\\\\\Rightarrow x=10.77

As the number of watches can not be in fraction, so at most she can buy 10 watches.

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Solve for equation √-5p=√24-p
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Answer:


Step-by-step explanation:

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p2-5p-24=0  

Two solutions were found :

    p = 8

    p = -3  

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2"   was replaced by   "p^2".  

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  p2-5p-24  

The first term is,  p2  its coefficient is  1 .

The middle term is,  -5p  its coefficient is  -5 .

The last term, "the constant", is  -24  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

      -24     +     1     =     -23  

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      -8     +     3     =     -5     That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  

                    p2 - 8p + 3p - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   p • (p-8)

             Add up the last 2 terms, pulling out common factors :

                   3 • (p-8)

Step-5 : Add up the four terms of step 4 :

                   (p+3)  •  (p-8)

            Which is the desired factorization

Equation at the end of step  1  :

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Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    p+3 = 0  

Subtract  3  from both sides of the equation :  

                     p = -3

Solving a Single Variable Equation :

2.3      Solve  :    p-8 = 0  

Add  8  to both sides of the equation :  

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