Question

chapter 1 review problems

1. $x - \frac{4}{7} = \frac{-3}{7}$
2. solve for x. $ax + b = 10$
3. you need to climb to the top of a house. you make measurements of the shadow of the house and find that it is 8.8m long. you then measure your shadow and it is 1.1m. you know you are 1.5 m tall. can you use a ladder that reaches 13m? (use proportions to find the height of the house)
4. double decker charges $10 a pizza and $1.50 per topping. tower pizza charges $12.50 a pizza and $1.00 a topping. how many toppings would make both pizzas cost the same? write the rule for each pizza place, then set them equal to each other to solve.

Explanation:

Step1: Isolate x by adding $\frac{4}{7}$

$x = \frac{-3}{7} + \frac{4}{7}$

Step2: Compute the fraction sum

$x = \frac{-3 + 4}{7} = \frac{1}{7}$

---

Step1: Isolate the ax term

$ax = 10 - b$

Step2: Solve for x (a≠0)

$x = \frac{10 - b}{a}$

---

Step1: Set up height-shadow proportion

$\frac{\text{House height }(h)}{\text{House shadow}} = \frac{\text{Your height}}{\text{Your shadow}}$
$\frac{h}{8.8} = \frac{1.5}{1.1}$

Step2: Solve for h

$h = \frac{1.5 \times 8.8}{1.1} = 1.5 \times 8 = 12$

Step3: Compare to ladder length

$12 < 13$

---

Step1: Define cost functions

Let $t$ = number of toppings.
Double Decker: $C_1 = 10 + 1.50t$
Tower Pizza: $C_2 = 12.50 + 1.00t$

Step2: Set costs equal, solve for t

$10 + 1.50t = 12.50 + 1.00t$
$1.50t - 1.00t = 12.50 - 10$
$0.50t = 2.50$
$t = \frac{2.50}{0.50} = 5$

Answer:

1. $\frac{1}{7}$
2. $\frac{10 - b}{a}$ (where $a

eq 0$)

1. Yes, the house is 12m tall, which is shorter than the 13m ladder.
2. 5 toppings