Lesson 9: Practice Problems

Problem 1

Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A’s?

Problem 2

Priya and Han are biking in the same direction on the same path.

Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after $t$ hours.
Priya started riding a half hour before Han. If Han has been riding for $t$ hours, how long has Priya been riding?
Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for $t$ hours.
Use your expressions to find when Han and Priya meet.

Problem 3

Which story matches the equation $- 6 + 3 x = 2 + 4 x$ ?

At 5 p.m., the temperatures recorded at two weather stations in Antarctica are -6 degrees and 2 degrees. The temperature changes at the same constant rate, $x$ degrees per hour, throughout the night at both locations. The temperature at the first station 3 hours after this recording is the same as the temperature at the second station 4 hours after this recording.
Elena and Kiran play a card game. Every time they collect a pair of matching cards, they earn $x$ points. At one point in the game, Kiran has -6 points and Elena has 2 points. After Elena collects 3 pairs and Kiran collects 4 pairs, they have the same number of points.

Problem 4

For what value of $x$ do the expressions $\frac{2}{3} x + 2$ and $\frac{4}{3} x - 6$ have the same value?

Problem 5 From Unit 4 Lesson 8

Decide whether each equation is true for all, one, or no values of $x$ .

$2 x + 8 = - 3.5 x + 19$
$9 (x - 2) = 7 x + 5$
$3 (3 x + 2) - 2 x = 7 x + 6$

Problem 6 From Unit 4 Lesson 6

Solve each equation. Explain your reasoning.

$3 d + 16 = - 2 (5 - 3 d)$
$2 k - 3 (4 - k) = 3 k + 4$
$\frac{3 y - 6}{9} = \frac{4 - 2 y}{- 3}$

Problem 7 From Unit 1 Lesson 7

Describe a rigid transformation that takes Polygon $A$ to Polygon $B$ .

A coordinate grid with polygon A in Quadrant II and polygon B in quadrant IV.