Kenneth S. answered • 02/24/16

Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018

Make 2 circles, partially overlapping, near the top of a page. Then make a third circle below both of these, overlapping both. The top two circles should be labeled C and H, from left to right (put these capital letters on the circumference, at top). Label the lower circle P (on circumference, at bottom).

Circle C can be viewed as having four distinct areas: Along top, from left to right: 15 & b

Beneath those, also L to R: a & c.

15 tells us that there are 15 parks having camping only; there are b parks having both Camping & Hiking

Beneath: a have Camping & Picknicking; c have all three (P, C, H)

In the upper right corner of the H circle, put 20 (20 parks have only Hiking); beneath that, place letter d in that region representing parks having Hiking and Picknicking.

Lastly, place 35 in the bottom part of circle P, for 35 parks having Picknicking only.

Now, if your picture is correct (i.e. if my instructions make sense to you), the following 4 given statements can be turned into equations:

185 had camping 185 = 15 + a +b +c

140 had camping and hiking trails 140 = b + c

125 Had camping and picnicking 125 = a + c

210 had hiking trails 210 = 20 + b + c + d

140 had camping and hiking trails 140 = b + c

125 Had camping and picnicking 125 = a + c

210 had hiking trails 210 = 20 + b + c + d

This linear system of 4 equations in four unknowns can be solved for a, b,c & d. Personally, I like to use the TI-83/84 MATRIX menu's RREF function on the equivalent Augmented Matrix. But you can use any method known to you.

David W.

02/24/16