At a birthday party pizzas and sodas were purchased for the kids. The number of sodas bought was two more than three times the number of pizzas. Pizzas cost $9.50 each and sodas cost $1.25 each.

30.5

Step-by-step explanation:

hope that helps

5 pizzas and 17 sodas were bought

Step-by-step explanation:

I don't have answers for a or b but I have them for c.

          Number of pizzas

      9.50n+1.25(3n+2)=68.75

         9.50+3.75n+2.50=68.75

           combine like terms

         13.25+2.5= 68.75

      subtract from both sides

     13.25=68.75-2.5

         13.35=66.25

            Divide

             n=5

         Number of sodas

        3n+2=3(5)+2=15+2=17

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

i think it is c, not positive though

step-by-step explanation: