Prealgebraic question

Topic : Word Problem on Dollors

Question : Ray had $5.12 to buy 79 cent postcards and 55 cent stamps, how many did he get?

Answer :

$5.12 = 512 cents
1 post card = 79 cents
1 stamp = 55 cents 55x + 79 y = 512
number of post cards(y) can not exceed 6 as 79 (7) = 553 > 512
and number of stamps ( x) can not exceed 9 as 55 (10) = 550 > 512
also x and y are integers > 0 .hence x can be 1,2,3,4,5,6,7,8,9 and y can be 1,2,3,4,5,6
55x ends with either 0 or 5
79 y ends with 9 ,8,7,6,5,4
a b c ---- 55x
d e f -----79y
---------
5 1 2
the sum of last digits of 55x and 79 y must be 2
hence we have only one such combination: 55x ends with 5 and 79 y ends with 7
if 79 y ends with 7 , then y must be 3 ( for 9 times 3= 27)
when y = 3 , 55x + 79(3)= 512 -> x = 5
so the number of stamps = 5
number of post cards = 3

Another way to Solve the same Problem.

Here there is another method to solve it without using algebra.
With 512 cents, he will try to buy maximum number of postcards
and maximum number of stamps.
For one postcard and one stamp, the cost is (79 + 55)= 134 centsNow 134 x 3 = 402.
So he buys 3 postcards and 3 stamps.
Now 512 - 402 = 110110 is divisible by 55. 110/55 = 2
So he can buy 2 stamps more.
Hence in total, he can buy 3 postcards and 5 stamps.

Logarithm Problem

Topic : Logarithm Problem

Question : Solve for x

Answer :