Question

Freddy the fruitseller receives a delivery of apples in a number of large crates, each containing 51 apples and 1 small container containing 39 apples. If Freddy wants to display the apples in boxes of 17 each, how many apples will be left over?

• A. 5
• B. 1
• C. 7
• D. 3

Answer 1

The correct option is A 5

We take:

$Totalnumberofapples=ANumberofdeliverycrates=CNumberofapplesineachcrate=51Numberofapplesinthesmallcontainer=39$

Hence, we get the total number of apples as:

$Totalnumberofapples=(51\times C)+39⟹A=51C+39$

Now, Freddy wants to display the same number of apples in boxes of 17 each, leaving some over.

$Numberofboxes=BTotalnumberofapples=(17\times B)+Leftover⟹A=17B+Leftover⟹51C+39=17B+Leftover$

Expanding the lefthand side of the equation, we get:

$51C+39=[17\times (3C\left)\right]+[17\times 2]+5=17[3C+2]+5$

$⟹17[3C+2]+5=17B+Leftover$
$⟹Leftover=5$