Question 1208259
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Hi
In a box there were some 50c coins and half as many 20cent coins. When 40 50c and 8 20cent coins were added.the value in the box would be 4 times as much as it was before.
What is the total value at first
What is the total of coins at the end.
This is word for word from textbook. 

Let original number of 20c coins be T
Then original number of 50c coins = 2T ({{{1/2}}} as many 20c as 50c, or # of 50c is TWICE the number of 20c)
Original value of 20c coins: $.2T
Original value of 50c coins: .5(2T) = $T
TRANSLATED, "When 40 50c and 8 20cent coins were added.the value in the box would be 4 times as much as
             it was before," gives us the following equation:
             T + 40(.5) + .2T + 8(.2) = 4(.2T)(T)
                   T + 20 + .2T + 1.6 = .8T<sup>2</sup>
                          1.2T + 21.6 = .8T<sup>2</sup>
                                    0 = .8T<sup>2</sup> - 1.2T - 21.6
                              {{{matrix(1,3, 2.5(0), "=", 2.5(.8T^2) - 2.5(1.2T) - 2.5(21.6))}}} -- Multiplying by {{{matrix(1,3, 10/4, or, 2.5)}}} to
                                                                                get rid of decimals 
                                    0 = 2T<sup>2</sup> - 3T - 54
                                    0 = 2T<sup>2</sup> - 12T + 9T - 54
                                    0 = 2T(T - 6) + 9(T - 6)
                                    0 = (T - 6)(2T + 9)
                                    0 = T - 6      OR     0 = 2T - 9
                                                   OR     9 = 2T
 
             Original number of 20c coins (T) = 6  OR   {{{matrix(1,4, T, "=", 9/2, "(IGNORE)")}}}
             Original number of 50c coins: 2T = 2(6) = 12
             Original number of coins: 6 + 12 = 18
 
             Number of 20c and 50c coins ADDED: 40 + 8 = 48
             <font color = red><font size = 4><b>Number of 20c and 50c coins AT END:</font></font></b> 18 + 48 = <font color = red><font size = 4><b>66</font></font></b>

             Original value of 20c coins: 6(.2) = $1.20
             Original value of 50c coins: 12(.5) = $6
             <font color = red><font size = 4><b>Original value of 20c and 50c coins:</font></font></b> $1.20 + $6 = <font color = red><font size = 4><b>$7.20</font></font></b></pre>