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A box containing 12 plates and 6 cups costs $156.00. Another box containing 12 plates and 18 cups of the same type costs $228.00. Find the cost of 9 plates.​



Answer :

Answer:

$90

Step-by-step explanation:

Solving the Problem

Setting Up the System of Equations

We can represent plates as p and cups as c. We can write the two sentences that describe the cost of plates and cups as

                                    [tex]12p+6c=156[/tex]

                                  ,[tex]12p+18c=228[/tex].

We're told to find the cost of 9 plates or 9p.

[tex]\dotfill[/tex]

Solving for 9p

There are many ways to get the value of p, we can use

  • the substitution method

(rearranging the variables in one equation and plugging that into the other one);

  • the elimination method

(subtracting the equations to get rid of an unnecessary variable).

For this case, we can use the elimination method, but we must have equivalent c terms.

We can multiply the first equation by 3 so both c terms are 18c.

                      [tex]3(12p+6c=156)=36p+18c=468[/tex]

Now, we can subtract each equation to eliminate the c values!

                              [tex]\:\:\:(36p+18c=468)\\\underline{-(12p+18c=228)}\\24p=240[/tex]

                                 [tex]p=10[/tex]

So, 9p = 9(10) = 90!

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