Arrange your own restaurant
Supposedly the ratio of the number of the tables to chairs in a restaurant is . I remove tables and chairs, and the new ratio is .
What is the total number of tables and chairs that are left?
The answer is 46.
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1 solution
Hello and peace be upon you,
Let t = tables , c = chairs,
as for initial ratios,
t : c = 4 : 9
t / c = 4 / 9
t = 4c / 9 ( 1st equation);
After removing tables and chairs,
t - 2 : c - 4 = 7 : 16
t - 2 / c - 4 = 7 / 16
16(t -2) = 7(c-4)
16t - 32 = 7c - 28
16t - 7c = 4(2nd equation),
substituting (1st) into (2nd) equation,
16( 4c / 9) - 7c = 4
64c - 63c = 36
c = 36
t = 4(36) / 9 = 16
total chairs and tables = 16 + 36 = 52,
but after removing 2 tables and 4 chairs = 52 - 2 - 4 = 46,
therefore, 46 is the answer,
thanks....