A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answers
Given:
A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same).
To find:
How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Solution:
From given, we have,
The number of trees is always the same, so, let the number of trees = x
A Blue Jay hides 18 acorns per tree, she will be left with four acorns
18x + 4 = 0 .....(1)
A Blue Jay hides 20 acorns per tree, she will be left with four spaces
20x - 4 = 0 ........(2)
equating equations (1) and (2), we get,
18x + 4 = 20x - 4
4 + 4 = 20x - 18x
8 = 2x
x = 4
Therefore, the number of trees is 4.
The number of acorns is given by,
18x + 4 = 18(4) + 4 = 72 + 4 = 76
OR
20x - 4 = 20(4) - 4 = 80 - 4 = 76
Therefore, the number of acorns is 76.
Therefore, 76 acorns is the Blue Jay going to store for the winter, and in 4 trees