Matemática Elementar

Problema 1

The table below shows the cost of apples at a market.

| Pounds | Cost ($) | |--------|-----------| | 2 | 3.00 | | 4 | 6.00 | | 6 | 9.00 | | 8 | 12.00 |

(a) Is the relationship between pounds and cost proportional? How do you know?

(b) What is the unit rate (cost per pound)?

Problemas

1. The table below shows the cost of apples at a market.

| Pounds | Cost ($) | |--------|-----------| | 2 | 3.00 | | 4 | 6.00 | | 6 | 9.00 | | 8 | 12.00 |

(a) Is the relationship between pounds and cost proportional? How do you know?

(b) What is the unit rate (cost per pound)?

2. A car travels $150$ miles in $2.5$ hours at a constant speed.

(a) Find the unit rate in miles per hour.

(b) How far will it travel in $4$ hours at the same speed?

3. On a scale drawing of a park, $1$ inch represents $40$ feet. A path on the drawing measures $3.5$ inches long.

(a) What is the actual length of the path in feet?

(b) A playground is actually $120$ feet wide. How wide is it on the drawing?

4. A store is having a $35\%$ off sale. A jacket originally costs $\$ 80$.

(a) How much is the discount?

(b) What is the sale price?

5. A savings account earns simple interest. After $1$ year, $500 grows to $530.

(a) How much interest was earned?

(b) What is the annual interest rate as a percent?

6. In a class of $30$ students, $18$ are girls.

(a) What percent of the class are girls?

(b) A neighboring class has the same percent of girls and has $25$ students total. How many girls are in the neighboring class? (Round to the nearest whole number.)

Gabarito — Proportional Relationships

1. (a) Check the ratio $\frac{\text{Cost}}{\text{Pounds}}$ for each row:

$\frac{3.00}{2} = 1.50, \quad \frac{6.00}{4} = 1.50, \quad \frac{9.00}{6} = 1.50, \quad \frac{12.00}{8} = 1.50$

All ratios are equal to $1.50$ . The relationship is proportional because the ratio is constant and the relationship passes through the origin.

(b) The unit rate is $\$ 1.50$ per pound.

(c) $C = 1.50p$

2. (a) Unit rate:

$\frac{150 \text{ miles}}{2.5 \text{ hours}} = 60 \text{ mph}$

(b) Distance in $4$ hours:

$60 \times 4 = 240 \text{ miles}$

(c) Time to travel $270$ miles:

$\frac{270}{60} = 4.5 \text{ hours}$

3. (a) Actual length:

$3.5 \text{ in} \times \frac{40 \text{ ft}}{1 \text{ in}} = 140 \text{ feet}$

(b) Drawing width:

$120 \text{ ft} \div \frac{40 \text{ ft}}{1 \text{ in}} = 3 \text{ inches}$

4. (a) Discount amount:

$35\% \times \$80 = 0.35 \times 80 = \$28$

(b) Sale price:

$\$80 - \$28 = \$52$

Alternatively: $65\% \times \$ 80 = 0.65 \times 80 = $52$.

5. (a) Interest earned: $530 - 500 = \$ 30$

(b) Interest rate:

$\text{Rate} = \frac{\text{Interest}}{\text{Principal}} = \frac{30}{500} = 0.06 = 6\%$

(c) Simple interest after $3$ years:

$I = P \times r \times t = 500 \times 0.06 \times 3 = \$90$

6. (a) Percent girls:

$\frac{18}{30} = 0.6 = 60\%$

(b) Girls in neighboring class:

$60\% \times 25 = 0.60 \times 25 = 15 \text{ girls}$