Question

4 + 2y = 9 + 2y

Answer 1

3(y – 5) + 2 = 5

Answer 2

70 = –7(–2 – 2z)

Answer 3

–6p + 7 = 3(2p – 3) – 4(–10 + 4p)

Answer 4

Ella and Margaret were at a carnival. They each got a ticket for the Ferris wheel. Ella got a snow cone, and Margaret got a cotton candy. Ella had a certificate for $6 off the cost. Margaret paid the rest, which came to $12.75. Each Ferris wheel ticket was $5, and a snow cone was $3.50. What was the cost for cotton candy?

Answer 5

To solve for y, we need to isolate the variable on one side of the equation.

Starting with the given equation, we have:
4 + 2y = 9 + 2y

Subtracting 2y from both sides of the equation:
4 + 2y - 2y = 9 + 2y - 2y
4 = 9

Since 4 does not equal 9, the equation has no solution.

Answer 6

Let's solve the equation step by step.

Starting with the given equation:
3(y – 5) + 2 = 5

First, distribute the 3 to the terms inside the parentheses:
3y - 15 + 2 = 5

Combine like terms:
3y - 13 = 5

Next, isolate the variable term by moving the constant term to the other side:
3y = 5 + 13

Simplifying the right side:
3y = 18

Finally, solve for y by dividing both sides by 3:
y = 18/3

y = 6

So, the solution to the equation is y = 6.

Answer 7

Let's solve the equation step by step.

Starting with the given equation:
70 = –7(–2 – 2z)

First, simplify the expression inside the parentheses:
70 = –7(-2 - 2z)
70 = 14 + 14z

Next, isolate the variable term by moving the constant term to the other side:
70 - 14 = 14z
56 = 14z

Finally, solve for z by dividing both sides by 14:
56/14 = z
4 = z

So, the solution to the equation is z = 4.

Answer 8

Let's solve the equation step by step.

Starting with the given equation:
–6p + 7 = 3(2p – 3) – 4(–10 + 4p)

First, simplify the expressions inside the parentheses:
–6p + 7 = 3(2p – 3) + 4(10 - 4p)

Next, distribute the coefficients to the terms inside the parentheses:
–6p + 7 = 6p - 9 + 40 - 16p

Combine like terms:
–6p + 7 = -10p + 31

Now, isolate the variable term by moving the constant term to the other side:
–6p + 10p = 31 - 7
4p = 24

Finally, solve for p by dividing both sides by 4:
p = 24/4
p = 6

So, the solution to the equation is p = 6.

Answer 9

Let's break down the information given in the problem step by step.

The price of each Ferris wheel ticket was $5.
Ella had a certificate that saved her $6 off the cost. Therefore, Ella paid $5 - $6 = -$1 for her ticket.
Since the cost of a ticket cannot be negative, we can assume that Ella's ticket was actually free.

Margaret paid the rest, which came to $12.75. This amount covers her Ferris wheel ticket and the cotton candy she purchased.
Let's subtract the price of the Ferris wheel ticket:
$12.75 - $5 = $7.75

This remaining amount must be the cost of the cotton candy.

Therefore, the cost for cotton candy was $7.75.