Ablue 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?

Remark

This is a nice problem especially if you like blue jays! They actually do things like this.

Equations.

Let the number of trees = T

Let the number of acorns = A

20*T = A + 4 Read that carefully. There are 4 acorns left over. The number stored = A. The left over ones make 4 more than were stored.

Second equation
18*T = A - 4 Here we have 4 less than could be stored to full capacity.

Solution

20T = A + 4

18T = A - 4 Subtract

2T = 8 Divide by 2

T = 8/2; T = 4 Answer

20T = A + 4

20*4 = A

80 - 4 = A

A = 76 Answer

Answers

The number of Trees = T

The number of acorns = 76

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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