4 A The perimeter of a rectangular garden

4 -A) The perimeter of a rectangular garden is 42 feet. The length of the garden is 5 feet more than twice the width. Which system of equations will determine the length, l, and the width, w, of the THE SECOND EQUATION IS garden? A) 2 l + w =42 C) 2 l + w WRITTEN USING THE FACT =42 2 w + l =5 THAT THE LENGTH IS 5 MORE THAN TWICE THE WIDTH: 2 l -w =5 B) 2 l + 2 w =42 D) 2 l + 2 w =42 l =5 -2 w E 2 l + 2 w =42 l =2 w + 5 l = 2 w + 5 D IS THE RIGHT ANSWER! w l = 2 w + 5 w =2 l -5 WE NEED TO USE THE INFORMATION GIVEN IN THE PROBLEM TO WRITE TWO l = 2 w + 5 EQUATIONS. THE FIRST EQUATION IS WRITTEN USING THE FACT THAT THE PERIMETER IS 42: 2 w + 2 l =42 OBJECTIVE 4 w

4 -B) On a trip Joel drove 25 miles more than half the number of miles Rita drove. Together they drove 340 miles. How many miles did Joel drive? F 130 mi G 170 mi H 195 mi J 210 mi K 315 mi WE USE THE FIRST SENTENCE TO WRITE ONE EQUATION: J = (1/2) R+ 25 25 miles more half the number of miles Rita drove WE USE THE SECOND SENTENCE TO WRITE ANOTHER EQUATION: J + R = 340 Together they drove 340 miles NOW, WE USE THE TWO EQUATIONS TO FIND HOW MANY MILES JOEL DROVE USING A T-I 82 CALCULATOR: OBJECTIVE 4

J = (1/2)R + 25 J + R = 340 Y = (1/2)X + 25 Y = 340 - X BEFORE WE CAN ENTER THESE EQUATIONS IN A TI- 82, WE NEED TO HAVE ONE VARIABLE ON ONE SIDE OF = BY ITSELF. IN THE SECOND EQUATION MOVE R TO THE RIGHT SIDE AND CHANGE ITS SIGN. WE ALSO LET J = Y AND R = X. 2)PRESS GRAPH. ZOOMED ONCE NOT ZOOMED 1)NOW WE ENTER THESE EQUATIONS IN A TI-82. PRESS Y= AND ENTER BOTH EQUATIONS. NOW, WE CALCULATE THE COORDINATES OF THE INTERSECTION POINT. 3) ZOOM OUT BY PRESSING ZOOM, 3, AND ENTER TWICE. YOU NEED TO ZOOM OUT UNTIL YOU SEE BOTH GRAPHS AND THEIR INTERSECTION ON THE SCREEN. ZOOMED TWICE ZOOMED 3 TIMES OBJECTIVE 4

4 -B) On a trip Joel drove 25 miles more than half the number of miles Rita drove. Together they drove 340 miles. How many miles did Joel drive? F 130 mi G 170 mi H 195 mi J 210 mi K 315 THIS IS THE SCREEN AFTER mi 5) PRESS 5, THEN ZOOMING 3 TIMES: ENTER 3 TIMES. THE CORRECT ANSWER ZOOMED 3 TIMES 4) PRESS 2 ND, THEN TRACE. THE COORDINATES ARE GIVEN AS: X=210 AND Y=130. BUT, WE KNOW THAT X=R AND Y=J. SO THE CORRECT ANSWER IS F 130 mi. REMEMBER YOU WERE ASKED TO FIND THE NUMBER OF MILES Joel DROVE. OBJECTIVE 4

4 -C) We use a TI-82 to answer this Question: 1) Enter the right side in Y 2 and the left side in Y 1: 2)Press 2 nd WINDOW and set the Tbl to 0. 5. OBJECTIVE 4 3)Look for the number in x column that makes the left side of > equal to the right side (use arrow up or Numbers above down!). 3 make the right side greater. 3 makes the two sides equal. Numbers below 3 (which are greater than 3!) make the left side greater than the right side. So, d is correct!

4 -C) Therefore the answer is d. We use a different method to answer 4 -C. 1)Enter the expressions in Y 1. To enter > press 2 nd , math, then 3. 2)Press GRAPH. 3)The graph shows all X’s that make the logical statement 4 x - 1 > 2 x + 5 a true statement; the graph of all X’s which make Y have a value of 1. These X’s are also the solutions of the inequality given. Note: When X is 3 Y is 0; This means that 3 is not a solution. To see this press 2 nd GRAPH. OBJECTIVE 4

End-of-Course Test Algebra I THIS IS THE END OF OBJECTIVE 4 REVIEW. YOU NEED TO WORK OUT THE PROBLEMS RELATED TO THIS OBJECTIVE. YOUR TEACHER WILL PROVIDE YOU WITH THE WORKSHEETS. WE WILL COVER OBJECTIVE 5 NEXT. CREATED BY R. KHADEM/ Adapted by Rene Patterson