Every year on November 1, the Stablo family plants a tree. This tradition has happened for generations and the first tree the family planted is now 183 years old. Two of the trees were planted in their backyard; one is an apple tree and the other is a maple tree. The maple tree is older than 100, but was not the first tree planted. On November 1 of this year, the age of the maple tree is fifteen times the age of the apple tree. On November 1 of some year from now, the age of the maple tree will be eleven times the age of the apple tree. How old are the trees that year?

Apple- 14 Maple- 154

Step-by-step explanation

Since 11 x n - n is equal to a number that ends in 10, 20 etc. and the number has to be a multiple of 11 for the maple tree, and the difference has to stay the same throughout two all we need to find is 15 x n = a number that is divisable by 10. 15 x 10 = 150 so that's the age of the trees this year, and the difference between the trees is 140 so it corresponds with our rule. and the multiple of 11 that the difference is 140 is 11 x 14 = 154 and 154 - 11 = 140. Therefore the apple tree is 14 years old and the maple tree is 154 years old.

sweetheart, there isn't a cube below.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal