Question 1208177
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Hi
Mr Thomas spent $1972 on cars and dolls. He bought 3 times as many cars as dolls. Each doll cost $10 more than each car. She paid $476 more for the cars than the dolls. What is the cost of a doll.

Let cost of ALL dolls purchased be x
Since $476 MORE was spent on cars than dolls, then amount spent on cars was x + 476
Since a total of $1,972 was spent, we get: x + x + 476 = 1,972
                                                    2x = 1,972 - 476
                                                    2x = 1,496
                              Cost of ALL dolls, or {{{matrix(1,5, x, "=", "1,496"/2, "=", "$748")}}}
                           So, cost of ALL cars = 1,972 - 748 = $1,224

Let price of each doll, be D
Then price of each car = D - 10

Number of dolls purchased: {{{748/D}}}
Number of cars purchased: {{{"1,224"/(D - 10)}}}
Since he bought 3 times as many cars as dolls, we get the following
NUMBER-OF-ITEMS equation:   {{{matrix(1,3, "1,224"/(D  -  10), "=", 3(748/D))}}}
                           {{{matrix(3,3, "1,224"/(D  -  10), "=", 3(748)/D,
12(102)/(D  -  10), "=", 3(4)(187)/D,
12(102)/(D  -  10), "=", 12(187)/D)}}}
                             {{{matrix(1,3, 102/(D  -  10), "=", 187/D)}}} --- Canceling GCF, 12, in numerators
                                102D = 187(D - 10) --- Cross-multiplying
                                102D = 187D - 1,870
                         102D - 187D = - 1,870
                               - 85D = - 1,870
            Cost of each doll, or {{{highlight_green(matrix(1,5, D, "=", (  -  "1,870")/(- 85), "=", highlight("$22")))}}}</pre>