civonamzuk

Triangles ABD and BCD are similar!!!

4 / BD = BD / 8

BD = √32  = 4√2 

360/28 = 55/x

x = (28*55)/360

The perimeter of triangle ABC = 1/2(78) 

Kumar bought 5 posters and 11 cards with 1/3 of his money. The cost of each poster was 3 times the cost of each card. He bought some more posters with 3/4 of his remaining money.

(a) What was the greatest number of cards Kumar could buy with 1/3 of his money?

(b) How many posters did Kumar buy in all?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 card = x          1 poster = 3x

5(3x) + 11x = 26x

a)    With 1/3 of his money, Kumar could've bought 26 cards.

b)    He bought 18 posters    

Your "challenging question" is incomplete!!! 

---------------------------------------------------------------

At first, Box F had 18 pears and 42 lemons while Box G had 36 pears and 50 lemons. Then, some lemons were moved from Box F to Box G and some pears were moved from Box G to Box F. In the end, Box F contained pears and lemons in the ratio 3:4 while Box G contained pears and lemons in the ratio 1:2.

(a)  In the end, how many lemons were in Box F?

(b)  In the end, how many more pears did Box G contain than Box F?

Smaller circle center => Q

∠LOQ = ∠MOQ = 1/2(arc 78º)

∠LQO = ∠MQO = 180 - 2(39) = 102

Arc LOM = 2 * 102 = 204 degrees

Marion had some money. She spent $210 on a watch and 1/10 of the remaining on a bracelet. If she had 3/8 of the original sum of money left, how much money did she have at first?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x - (210 + 1/10(x - 210)) = 3x/8

x = 360

Marion had $360

Three boys have the same number of blue toy cars. 1/4 of Nelson's toy cars and 4/5 of Ted's toy cars and of 2/3 Kieran's toy cars are blue. The total number of toy cars that are not blue is 75. How many toy cars does Ted have?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3x + x/4 + x/2 = 75

x = 20           (Each boy has 20 blue toy cars)

Ted has 25 toy cars 

This one's quite tough. 

6th piggy bank = 3 * 81  

Very important text:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Keith and Lucas each had a mix of twenty-cent and one-dollar coins. Keith had 16 one-dollar coins...

(c) Keith used half of his one-dollar coins and some of his twenty-cent coins to buy a book that cost $10.40. Then, he had 7/10 of his twenty-cent coins left. How many twenty-cent coins did Keith have at first?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1/  Keith had 16 one-dollar coins                                                                   => 16 coins

2/  He spent 8 one-dollar coins and 12 twenty-cent coins to buy a book.     =>  12 coins

3/  After he bought a book, Keith had 7/10 of his twenty-cent coins left.       =>  28 coins

12 / (3/10) = x / (7/10)         x = 28

Keith had 40 twenty-cent coins and 16 one=dollar coins.

Remember, all 3 boys had an equal number of coins.