Question

There are two types of nuts, 125 cashews and 288 almonds in a box. You take away 195 nuts. How many nuts are left in the box?

• A. $431$
• B. $281$
• C. $413$
• D. $218$

Answer 1

The correct option is D $218$

To find the total number of nuts, we add 125 and 288 by expansion method.
$\bullet$ We expand 125 and 288 as follows:
$288=200+80+8$
$125=100+20+5$

$\bullet$ For ones place, we add 8 and 5 to give 13 or 13 ones.
$8+5=13$
13 ones can be regrouped as 1 tens (10) and 3 ones (3).
$\bullet$ For tens place, we add 10, 80, and 20.
$10+80+20=110$
110 can be regrouped as 1 hundred (100) and 1 tens (10).
$\bullet$ For hundreds place, we add 100, 200, and 100.
$100+200+100=300$
$\bullet$ Hence, we get $288+125=413$.
$\bullet$ There are a total of 413 nuts in the box.

To find the number of nuts left in the box, we subtract 195 from 413 using the expansion method.
$\bullet$ We expand 413 and 195 as follows:
$413=400+10+3$
$195=100+90+5$


$\bullet$ The ones place has 3 ones and 5 ones.
$\bullet$ The number in the next higher place is 10. Hence, to subtract we regroup as follows:
$\to$ 10 is taken from tens place and added to ones place.
$\to$ In ones place, we get $10+3=13$.
The ones place now has 13 and 5 .
Subtracting 5 from 13, we get $13-5=8$.
$\to$ In tens place, we get $10-10=0$.
The tens place now has 0 and 90.
To subtract 90 from 0, we regroup.
100 is taken from hundreds place and added to tens place.
We get, $0+100=100$.
The tens place now has 100 and 90.
Subtracting 90 from 100, we get 100 − 90 = 10.
In hundreds place, we get 300 − 100 = 200.
$\bullet$ $200+10+8=218$
$\bullet$ Hence, $413-195=218$.
$\bullet$ There are 218 nuts left in the box.
$\bullet$ Option B is the correct answer.