Pizza
Number Theory
Level
4
On Sunday, a pizza store produces pizzas in batches of 68, and usually make between 1000 and 1500 pizzas. The store only sells pizza in batches of 20.
At the end of the day, if the store is left with 32 pizzas, how many pizzas were sold?
The answer is 1260.
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1 solution
Let the number of pizzas be 6 8 x as pizzas are produced in batches of 6 8 . The same number is equal to 2 0 y + 3 2 as the pizzas are sold in batches of 2 0 and still 3 2 are left.
Since 6 8 x lies in the range ( 1 0 0 0 , 1 5 0 0 ) , x lies in the range ( 1 5 , 2 2 ) ,
Since 2 0 y + 3 2 ends in 2 , the only multiple of 6 8 in the range is 6 8 × 1 9 = 1 2 9 2 .
The pizzas sold= 1 2 9 2 -pizzas left= 1 2 9 2 − 3 2 = 1 2 6 0