Question

assignment - equations & inequalities, day 6
real - world multi - step problems
algebra i
recall

1. what is the solution for the equation?

-4(2h - 9)=5(2h + 6)
today
define the variable, write an equation or inequality, and solve.

1. victor bought a video game and two controllers for $59.97. leonardo rented the game for three days at $7.99 per day, and he bought three controllers. if victor and leonardo spent the same amount, what is the cost of each controller?
2. parker has $720 in his bank account. he spends $35 each week on food. jack has $145 in his account and deposits $80 each week. after how many weeks will jack have at least as much money as parker?
3. a rectangle has a length of (5x + 10) inches and a width of 5 inches. a parallelogram has a base of (10x - 12) inches and a height of 6 inches. the area in square inches of the rectangle is equal to the area in square inches of the parallelogram. what is the value of x?
4. candi has crates that weigh 50 pounds each, plus a box that weighs 17.5 pounds. manny has crates that weigh 50 pounds each, plus one box that weighs 97.5 pounds. how many crates will it take for candi to have more weight of crates and boxes than manny?

all year

1. use the number line to represent the solution set for -4x + 10≥5x + 55.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Explanation:

1.

Step1: Expand both sides

$-4(2h - 9)=-8h + 36$, $5(2h + 6)=10h+30$

Step2: Set up new - equation

$-8h + 36=10h + 30$

Step3: Move terms with h to one side

$-8h-10h=30 - 36$

Step4: Combine like - terms

$-18h=-6$

Step5: Solve for h

$h=\frac{-6}{-18}=\frac{1}{3}$

2.

Step1: Set up the equation

Victor's cost is the cost of the game plus 2 controllers, $59.97 + 2x$. Leonardo's cost is the rental cost of the game for 3 days plus 3 controllers, $3\times7.99+3x$. Since they spent the same amount, $59.97 + 2x=3\times7.99+3x$.

Step2: Simplify the right - hand side

$3\times7.99 = 23.97$, so the equation is $59.97+2x=23.97 + 3x$.

Step3: Move terms with x to one side

$59.97-23.97=3x - 2x$.

Step4: Solve for x

$x = 35$.

3.

Step1: Set up the inequality

Parker starts with $720$ and spends $35$ per week, so his amount of money after $w$ weeks is $720-35w$. Jack starts with $145$ and deposits $80$ per week, so his amount of money after $w$ weeks is $145 + 80w$. We want to find when Jack has at least as much as Parker, so $145 + 80w\geq720-35w$.

Step2: Move terms with w to one side

$80w+35w\geq720 - 145$.

Step3: Combine like - terms

$115w\geq575$.

Step4: Solve for w

$w\geq\frac{575}{115}=5$.

4.

Answer:

$h = \frac{1}{3}$