# Math

Mr. Badger bought 12 pens every month until their price rose to 15 cents each. Now he can only afford to buy 10 pens at the same total cost as before. What was the original price of each pen?

There are 41 pigs and chickens on a farm. If there are 100 legs counted altogehter, how many of each animal are there?

One day, 5/6 of the office staff came to work. If three more had been away, this fraction would have decreased to 3/4. How many people are on full staff?

Mrs. Grant was 20 when her eldest child, tess, was born. Carly was born 2 years later and Troy another 4 years later. Now the average of their four ages is 39. How old are Mrs. Grant and her three children?

1. 2. We have X pigs and Y chickens.
Eq1: X + Y = 41 Pigs and chicken.

Each pig has 4 legs and each chicken has 2 legs:
Eq2: 4X + 2Y = 100 Legs.

Multiply both sides of Eq1 by -2 and

-2X - 2Y = - 82,
4X + 2Y = 100,

2X = 18,
X = 9 Pigs.

Substitute 9 for X in Eq1:
9 + y = 41,
Y = 41 - 9 = 32 Chickens.

3. 5X/6 - 3 = 3X/4,
Multiply both sids by 12:
10x - 36 = 9X,
10X - 9X = 36,
X = 36 Staff members.

4. Tess: X Years old.
Mrs. Grant: X+20.
Carly: X-2.
Troy: X-6.

(X + (X+20) + (X-2) + (X-6)) / 4 = 39,
(4X + 12) / 4 = 39,
Multiply both sides by 4:
4X + 12 = 156,
4X = 156 - 12 = 144,

X = 36 = Tess's age.
X+20 = 36+20 = 56 = Mrs. Grant's age.
X-2 = 36-2 = 34 = Carly's age.
X-6 = 36-6 = 30 = Troy's age.

posted by Henry

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