Understanding multi-step problems involving non-linear equations in one variable

Garrett can row 5 miles per hour in still water. It takes him the same amount of time to row 4 miles upstream as it does to row 16 miles downstream. What is the speed of the current?

• 4 mph

• 3 mph

• 2.4 mph

• 2.86 mph

The length of a rectangle is 7 feet shorter than twice its width. Its area is 100. Which equation can be used to solve for x?

•  $x\left(2x-7\right)=100$ 

•  $2x-7=100$ 

•  $\left(x-7\right)\left(2x\right)=100$ 

•  $x\left(x-7\right)=100$ 

Twenty years ago, Mr. Stern purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

• $176,783.29
• $424,527.63
• $57,357.75
• $532,041,076.80

Typically in a percent problem, what follows the word OF?

ex: 50% OF _______ is 36.

• whole

• part

• percent

Trent's grandmother baked 5 pies. Each pie is divided into 8 pieces.

Trent's family eats the same number of pieces of pie each day. How many pieces did they eat if all the pieces were eaten in 4 days?

• 40

• 13

• 10

• 4

It takes Jeremy 1/3 of an hour to paint 1 painting. How many paintings can he paint in 9 hours?

• 25
• 27
• 1/27
• 1/25

I have 20 roses and 5 daisies. I make vases of flowers. Each vase is the same. What is the greatest number of vases can I make?

• 15

• 5

• 25

• 10

It takes about 90 days for a drop of water to travel the length of the Mississippi River. The Mississippi River starts in Minnesota and flows 2,340 miles south to its outlet in which state - Louisiana or South Carolina?

• Louisiana

• South Carolina

Translate:  The sum of 30 and a number squared is 100.

• 30 - x^2 = 100
• (30 + x)^2 = 100
• 30 + x^2 + 100
• 30 + ^x^2 = 100

The product of two consecutive integers is 168. Which of the following quadratic equations correctly represents this situation?

• x² + 2x - 168 =0

• x² + x + 168 =0

• x² + x - 168 =0

Answer explanation

Let the two consecutive integers be x, x+1 x ( x+1) = 168 x² + x = 168 x²+ x - 168 = 0 So the correct option is option 3. If Option 2 is chosen, then it is incorrect as the sign of 168 was not changed while transposing it to the LHS. If Option 1 is chosen, then it is also incorrect as instead of two consecutive integers x and x+1, x and x+2 were considered while formulating the equation.