Final Exam Review #9

Final Exam Review #9

Word problems

The product of 2 positive consecutive odd integers is 323. If x represents the smaller integer, determine the value of both integers.

• Think: If x is the smallest, what would represent the next one?

• We will need some vocabulary for that...

Vocabulary

• product - when I multiply

• consecutive - in a row

• odd - (for example) 1, 3, 5, 7, 9 etc

• So if x was 5, the next one is 7. How did we get there? x + 2

• So use the vocabulary to rewrite the question... When I multiply two positive numbers in a row (x) and (x+2), I get 323.

• Mathematically that looks like (x)(x+2) = 323

Solving (x)(x+2)=323

• Distribute x² + 2x = 323

• Write in standard form equal to zero x²+ 2x - 323 = 0

• Solve with the quadratic formula $\ \ \ \ x\ =\ \frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

• a = 1, b= 2, c = -323

Solve

•  $x=\frac{-\left(2\right)\pm\sqrt{\left(2\right)^2-4\left(1\right)\left(-323\right)}}{2\left(1\right)}$  

•  $x=\frac{-2\pm\sqrt{4+1292}}{2}$  

•  $x=\frac{-2\pm\sqrt{1296}}{2}\ =\ \frac{-2\pm36}{2}$  

•  $x=\frac{-2+36}{2}=\frac{34}{2}=17\ \ \ or\ \ x=\frac{-2-36}{2}=-\frac{38}{2}=-19$  

• Which answer fits the problem? Remember we were looking for two positive numbers so x must be 17 and x+2 must be 19. Multiply to check.

Multiple Choice

The product of 2 positive consecutive odd integers is 143. If x represents the smaller integer, determine the value of both integers.

• 11 and -13

• 11 and 13

• 11

• 13

Multiple Choice

The product of 2 positive consecutive odd integers is 575. If x is the smallest integer, determine the value of the largest integer.

• 23

• 23 and 25

• 25

• 27

• 25 and 27

Fill in the Blank

2. Find two consecutive positive even integers whose product is 224.

(Separate your answer with a comma, and no spacing.)

Multiple Choice

The sum of 3 consecutive numbers is 36. If x represents the smallest number, find the middle number.

• 14

• 13

• 10

• 11

• 12

Multiple Choice

If the sides (x) of a square are increased by 2 inches, the area becomes 81 square inches. Determine the length of the sides of the original square.

• 81

• 9

• 7

• 49

Multiple Choice

If the sides (x) of a square are decreased by 4 inches, the area becomes 36 square inches. Determine the length of the sides of the original square.

• 2

• 10

• 6

• 8