Question

the cost for 7 dance lessons is $82, the cost for 11 lessons is $122. write a linear equation to find the total cost (c) for (l) lessons. then use the equation to find the cost of 4 lessons.

Answer 1

To find the total cost of dance lessons, a linear equation was created using the given costs for different numbers of lessons, resulting in c = 10l + 12. Using this equation, the cost for 4 lessons was calculated to be $52.

Step-by-step explanation:

The cost for 7 dance lessons is $82, and the cost for 11 lessons is $122. To write a linear equation for the total cost (c) for a number of lessons (l), we first find the cost per lesson and then incorporate any fixed costs.

Step 1: Determine the cost per lesson by finding the difference in costs and dividing by the difference in the number of lessons.

• Cost difference: $122 - $82 = $40
• Lesson difference: 11 - 7 = 4
• Cost per lesson: $40 / 4 = $10

Step 2: Use one of the given points to solve for any fixed cost.

• $82 = 7 lessons x $10/lesson + fixed cost
• Fixed cost = $82 - (7 x $10) = $82 - $70 = $12

Step 3: Write the equation c = 10l + 12, where c is the total cost and l is the number of lessons.

Step 4: To find the cost of 4 lessons, plug l = 4 into the equation:

• c = 10(4) + 12
• c = $40 + $12
• c = $52

The total cost for 4 lessons is $52.

Answer 2

(7,82)(11,122)
slope = (122-82)/(11-7) = 40/4 = 10

y = mx + b
slope(m) = 10
(7,82)...x = 7 and y = 82
now we sub and solve for b, the y int
82 = 10(7) + b
82 = 70 + b
82 - 70 = b
12 = b

so ur equation is : y = 10x + 12

when x = 4
y = 10(4) + 12
y = 40 + 12
y = 52 <== total cost is 52 for 4 lessons