6: Ratio and Rate Reasoning
A car travels 90 miles on 3 gallons of gas. What is the unit rate?
30 miles per gallon
Which is smaller: −2 or −9?
−9
y = 5x. What is y when x = 4?
20
5x − 3 = 17
4
x³ × x⁴
x⁷
The ratio of cats to dogs is 2:3. There are 10 cats. How many dogs are there?
15 dogs
What is |−13|?
13
A graph passes through (3, 12). Is this proportional? What is k?
Yes. k = 12/3 = 4
2(x + 6) = 20
4
x⁸ ÷ x³
x⁵
A recipe uses 4 cups of flour for every 6 cookies. How many cups are needed for 24 cookies?
16 cups
Order from least to greatest: −5, 2, −1, 0, −8
−8, −5, −1, 0, 2
x: 2, 4, 6 | y: 9, 18, 27
Yes. k = 9/2 = 4.5
3x + 5 = x + 19
7
(x³)⁴
x¹²
The ratio of boys to girls is 4:5. There are 36 students total. How many are girls?
20
What is the distance between −6 and 4 on a number line?
|4 − (−6)| = 10 units
y = kx. When x = 7, y = 42. Find y when x = 11.
k = 6. y = 6 × 11 = 66
4(x − 2) = 2x + 6
7
5⁰ + 2⁻¹
1 + 1/2 = 3/2
A store sells 3 notebooks for $7.50. Another sells 5 for $12.00. Which is the better deal?
Store 2. $2.40
Point A is at −3 and Point B is 7 units to the left. What is Point B's location?
−3 − 7 = −10
A car uses fuel at a proportional rate. At mile 60, it has used 4 gallons. How many gallons at mile 105?
k = 60/4 = 15 miles/gal. 105 ÷ 15 = 7 gallons
3 − 2(4x − 1) = x − 10
5/3
(3x²)³ ÷ x²
27x⁴