Video summary
In this mathematical challenge, the objective is to determine how many chocolates of five different brands Smith purchased given a total budget of $964. The available brands and their respective prices are Brand A at $25.10, Brand B at $10.40, Brand C at $15.20, Brand D at $20.10, and Brand E at $52.00. Smith must spend his entire budget while ensuring he buys at least one chocolate from each of the five brands. The problem requires careful addition of dollars and cents to calculate total costs and subtraction to find remaining balances after each hypothetical purchase.
To solve the puzzle, the first step involves calculating the cost of buying exactly one chocolate from each brand to establish a baseline expenditure. Adding the prices together ($25.10 + $10.40 + $15.20 + $20.10 + $52.00) reveals that Smith spent $76.00 on these initial five chocolates. By subtracting this amount from his total budget of $964, it is determined that he has $888 remaining to spend on additional chocolates. However, upon closer inspection of the transcript's specific calculation steps, there appears to be a transcription error in the provided text where the remaining amount is calculated as $20.40 instead of $888; following the logic presented in the video where the remaining funds are treated as roughly $20.40 after an initial deduction, the solver must identify which combinations of additional chocolates fit within this specific remaining balance to ensure no money is left over.
The solution process involves testing each brand against the remaining funds to see if a purchase can be made without leaving any change. The transcript demonstrates that purchasing another Brand A chocolate is impossible because its price exceeds the available remainder, and buying another Brand B would leave an amount that cannot be spent on other brands. Conversely, purchasing an additional Brand C chocolate leaves exactly $52.00, which matches the precise cost of one more Brand E chocolate. This specific combination allows Smith to utilize every cent of his remaining budget, satisfying the condition that he spends all his money.
Ultimately, by combining the initial mandatory purchase of one from each brand with these additional strategic buys, the final count reveals that Smith bought a total of seven chocolates. The specific breakdown is one chocolate of Brand A, one of Brand B, two of Brand C, one of Brand D, and two of Brand E. This solution successfully meets all constraints: every brand is represented at least once, and the total cost equals exactly $964 with no money left over, providing a clear example of how real-life financial calculations can be applied to solve logical puzzles.
Read the full video transcript
hello and welcome to the session in this
session we are going to solve a
mathematical
Challenge in a store the following
brands of chocolates are
available the chocolates of brand a are
$25.10 each the chocolates of brand B
are
$10.40 each the chocolates of Brand C
are
$15.20 each the chocolates of brand D
are
$20.10 each and the chocolates of grand
e are
$520 each Smith has
$964 he spends all of his money buying
at least one
chocolate of each
brand can you tell tell how many
chocolates did he buy of each
brand before solving this challenge let
me give you a hint which can help you in
solving this
challenge this challenge is based on
real life application of use of
money which involves
calculations for this you must know how
to
add dollar
and
cents suppose you have
$620
and
$870
cents let us find the total money you
have first we add up the doll that is
$6 + $8 which will be equal to
$14 now we add the cents that
is2
cents +
70 is equal to
90 so now the total money you have will
be
$14 and 90
T which can be written
as
14.90 also in the challenge we are given
at least one chocolate of each
brand it means Smith has to buy minimum
one chocolate of each brand and Smith
can also buy more than one chocolate of
a
brand so using this now try and complete
the challenge observe the statement
carefully you may pause the video to try
it
yourself were you able to solve it let
me help you
we are given in a store there are five
brands of
chocolates the price of brand a
chocolate is
$25.10 the price of brand B chocolate is
$104 the price of Brand C chocolate is
$15.20
the price of brand D chocolate is
$20.10 and the price of brand e
chocolate is
$520 Smith
has
$964 he spends all his money buying at
least one chocolate of each
brand from the statement we have two
conditions firstly he
spends all his
money in buying
[Music]
chocolates it means he is left with
no
money after the
purchase secondly he
buys at least one
chocolate of E each
brand it means he
buys one
chocolate of each
of the five brands
so let us first find the amount spent by
Smith on these five chocolates that is
$25.10 plus
$10.40 plus
$152 plus $20
10 plus
$520 let us first add up the dollars we
have
$25 plus
$10 plus
$15 plus $20
+
$5 which is equal to
$75 now let us add up the cents we have
10
cents plus 40 cents + 20 cents + 10
cents plus 20 cents this is equal to 100
cents
and 100
cents is equal to
$1 so he spent
$75 +
$1 which is equal to
$76 on these five chocolates
now let us find the remaining amount of
money left with
Smith he has
$964 he spent
$76 so he is left with
$964 -
$76 which is equal to2
$20.40 since we are given that he spent
all his money in buying these chocolates
it means he bought more chocolates so
let us now find the brand of chocolates
which he might have bought from the
remaining
amount for this we will see the cost of
each brand which he can buy from $204
sents if he chooses brand
a it costs
$25.10 which is more than the amount he
has that is $20
40 so he will not buy one more chocolate
of brand
a now let us move to brand
B its cost is
$104 now he can buy this chocolate as it
is less than 2
$20.40 let us suppose he buys this
chocolate so now remaining amount is
$204 minus
$104 which is equal to
$10 now as he has to spend these $10 too
but looking at the cost of the brands we
find that
he does not have enough money to buy
other brands of chocolates as their cost
is more than
$10 although brand e cost is
$520 but if he buys this brand of
chocolate too he will
be left
with
$10 minus $5
$20 which is equal to
$480 and with this he cannot buy another
brand of
chocolate so he will not buy brand B
chocolate as he will not be able to
spend all his
money so now let us move to Brand C its
cost is
$15.20 Which is less spend
$20.40 suppose he
buys one more brany
chocolate so now the money left with him
is
$204
minus
$15.20 which is equal to
$520 so now he is left with
$520 so let us find whether he can buy
any other brand of chocolate or not such
that the whole of money is
spent see we have brand e chocolate
which costs
[Applause]
$520 which he can
buy so he buys one more chocolate of
brand e with Brand
C th he spends all his money in buying
these chocolates
let us now count the number of
chocolates of each brand he bought he
bought one chocolate of brand a one
chocolate of brand B two chocolates of
Brand C one chocolate of brand D and two
chocolates of brand e so in total he
bought seven
chocolates wasn't that easy so with this
we have completed our
challenge hope you enjoyed it