Solve the following

Question

Solve the following

1. A well is 20 feet deep. A snail at the bottom climbs vertically up 4 feet each day and slips back 2 feet each night. How many days will it take the snail to reach the top of the well?

2. Sheena picked a basket of guavas. She gave half of the guavas to her neighbor, 8 guavas to her mother and half of the remaining guavas to her bestfriend.she kept 3 guavas for herself. How many guavas did she have at the beginning?

3. There were 61 athletes at the annual sports fest who plays for either the basketball team and 18 were in the baseball team,how many players were both in teams

4 the sum of 10 consecutive counting numbers is 155.if the least number is taken away, the average becomes 16.if 6 is added to the remaining 9 numbers.what is the new average?

5. Tom has just enough money to buy exactly 11 apples and 3 mangoes or exactly 2 apples and 5 mangoes. Danny wants only one type of fruit and has enough money to buy 1 mango but not enough for 2, or enough money to buy x apples. Find the greatest possible value of x.

Answer 1

2. Sheena picked a basket of guavas. She gave half of the guavas to her neighbor, 8 guavas to her mother and half of the remaining guavas to her bestfriend.she kept 3 guavas for herself. How many guavas did she have at the beginning?

I would work backwards on this problem.

Sheena has 3 guavas left after giving half of the remaining guavas to my best friend.

That means her best friend also has 3 guavas.

Sheena gave 8 to her mother.

The total of Sheena's (3), her friend's (3) and her Mother's (8) is 14.

That total was half what she started with. She gave the other half to her neighbor, so he also had 14 guavas.

Add the two halves together and you will know that Sheena started with 14+14 which equals 28 guavas.

Answer 2

1) If the snail gains 4 ft/day and loses 2 ft/night, then the net result is a gain of 2 ft.

The well is 20 ft. deep so it would take 20 ft x 1day/2ft. = 10 days to reach the top.

2) Let x = no. guavas at the start. Then x = the sum of the qty given to the neighbor + the 8 for her mother + those given to her best friend + 3 for herself.

So x = x/2 + 8 + 1/2[x - (x/2 + 8)] + 3

x/2 is given to the neighbor, the 8 is for her mother, the best friend gets 1/2 of the remainder (3rd term) and the 3 is for herself.

x = x/2 + 8 + x/2 - x/4 - 4 + 3

x = x/2 + x/2 - x/4 + 7 Mult by 4 to remove fractions: 4x = 2x + 2x - x + 28

4x = 3x + 28; x = 28 guavas

Check: 28 - 14 to neighbor = 14; 14 - 8 to mother = 6; 6 - 3 to best friend = 3 left for herself.

4) If take away the least of 10 consecutive numbers and the new avg, is 16, then new sum is 16 x 9 = 144.

So the least no. must have been 155 - 144, or 11 and the original series was 11,12,13,14,15,16,17,18,19,20 totaling 155. The new series with 9 nos. totals 144. If add a 6 , new total is 150 for 10 nos., avg. is 15.