SOLUTION: These questions are making me confused. 1.The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of t

Question 1045436: These questions are making me confused.
1.The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
2. Kelly, Laura, and Tia sold boxes of cookies for a fundraiser. Kelly sold 15 boxes less than Laura. Tia sold twice as many boxes as Kelly. If they sold 83 boxes in total, how many boxes did each girl sell?
3. The measure of the vertex angle in an isosceles triangle is six less than four times the measure of a base angle. Find the measure of the vertex angle.

Found 2 solutions by Alan3354, jorel555:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1.The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
---
P = 2W + 2L = 62
W + L = 31
---
L = 4W+1
Sub for L
W + 4W+1 = 31
5W = 30
W = 6, L = 25
======================
2. Kelly, Laura, and Tia sold boxes of cookies for a fundraiser. Kelly sold 15 boxes less than Laura. Tia sold twice as many boxes as Kelly. If they sold 83 boxes in total, how many boxes did each girl sell?
K = L - 15
T = 2K = 2L - 30
K + L + T = 83
----
L-15 + 2L-30 + L = 83
4L - 45 = 83
L = 32
etc.
======================
3. The measure of the vertex angle in an isosceles triangle is six less than four times the measure of a base angle. Find the measure of the vertex angle.
---
There are 2 base angles.
B + B + V = 180
V = 4B - 6
Can you do the rest?
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
1.P=2L+2W
62=2W+2(4W+1)
=10W+2
10W=60
W=6
L=25.
2.Let k represent Kelly. Then Laura is k+15, and Tia is 2k. So:
k+k+15+2k=83
4k=68
k=17
Kelly sold 17, Laura sold 32, and Tia sold 34.
3.Let b represent a base angle. Then the vertex angle is 4b-6. So
2b+4b-6=180
6b=186
b=31
4b-6=118. ☺☺☺☺
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