Question

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 Blue Jay going to store for the winter, and how many trees?

Answer 1

Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

$18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4$

There are 4 trees, and there are $18x+4$ acorns or 76 acorns.

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Answer 2

Answer:

76 acorns and 4 trees

Step-by-step explanation:

Let X be the number of acorns (a) Ms. Blue Jay plans to store.

We are told that she could hide 18 acorns (a) per tree (t) which we'll write as 18a/t.  This would result in 4 leftover acorns.

We then learn that if she hides 20 acorns per tree, 20a/t, she will have space for an extra four acorns.

There are t trees in both cases.  We can write these two scenarios as:

1)  18t + 4  = X [18 acorns are in each tree, t, plus there are 4 left over.]

2)  20t -4  = X [20 acorns per tree, t, with room to store 4 more]

These two are equal to each other:

18t + 4 = 20t - 4

2t = 8

t = 4

There are 4 trees.

Since 18t+4 = X, the total number of acorns is18*4+4 = 76 acorns and 4 trees.

Check to see if 76 acorns works for the second scenario:

Will hiding 20 acorns per tree leave room for 4 acorns if there are 76 acorns?

(4 trees)*(20 acorns/tree) = 80 acorns can be stored.  If Ms. Jay only has 76 acorns, there will be room for 4 more acorns.