Kayla purchased 5 large sodas at the movie theater. Before tax was added, the total cost of the 5 sodas was equal to the cost of 3 sodas plus $7. What was the cost of one soda, s?

Answer 1

Let the cost of one soda be \( s \).

According to the problem, the total cost of 5 sodas can be expressed as:

\[ 5s \]

We are also told that this total cost is equal to the cost of 3 sodas plus $7. The cost of 3 sodas can be expressed as:

\[ 3s + 7 \]

Setting the two expressions for the total cost equal to each other, we have:

\[ 5s = 3s + 7 \]

To solve for \( s \), subtract \( 3s \) from both sides:

\[ 5s - 3s = 7 \]

This simplifies to:

\[ 2s = 7 \]

Now, divide both sides by 2:

\[ s = \frac{7}{2} = 3.5 \]

Thus, the cost of one soda is

\[ \boxed{3.50} \]

Answer 2

Katherine works flexible hours. This month she worked a total of 60 hours, which was 3 more than 5 times as many hours as she worked last month. How many hours did she work last month?

Answer 3

Let \( x \) represent the number of hours Katherine worked last month. According to the problem, the total hours she worked this month is given by the equation:

\[ 60 = 5x + 3 \]

To solve for \( x \), first subtract 3 from both sides:

\[ 60 - 3 = 5x \]

This simplifies to:

\[ 57 = 5x \]

Next, divide both sides by 5:

\[ x = \frac{57}{5} = 11.4 \]

Thus, the number of hours Katherine worked last month is

\[ \boxed{11.4} \]

Answer 4

Matt is saving for college. He puts $20 in his savings account each week. How many weeks, w, will it take for him to save $15000?

Answer 5

Matt saves $20 each week. We can set up the equation to find out how many weeks \( w \) it will take for him to save $15,000 using the equation:

\[ 20w = 15000 \]

To solve for \( w \), divide both sides of the equation by 20:

\[ w = \frac{15000}{20} \]

Now, perform the division:

\[ w = 750 \]

Thus, it will take Matt

\[ \boxed{750} \]

weeks to save $15,000.

Answer 6

A cell phone company charges a shipping fee of 7% of the purchase cost, p. If the total cost of shipping is calculated to be $30.25, what is the purchase price before shipping was added?

Answer 7

The shipping fee is given as 7% of the purchase cost \( p \). The total shipping fee can be expressed as:

\[ 0.07p \]

According to the problem, this shipping fee amounts to $30.25. Therefore, we can set up the equation:

\[ 0.07p = 30.25 \]

To find the purchase price \( p \), divide both sides by 0.07:

\[ p = \frac{30.25}{0.07} \]

Now, perform the division:

\[ p = 432.14 \]

Thus, the purchase price before shipping was added is

\[ \boxed{432.14} \]

Answer 8

If the perimeter of a rectangle is 60 ft and its length is 18 ft, find its width. (see formula in number 1)

Answer 9

The perimeter \( P \) of a rectangle can be calculated using the formula:

\[ P = 2L + 2W \]

where \( L \) is the length and \( W \) is the width.

Given that the perimeter is 60 ft and the length is 18 ft, we can substitute these values into the formula:

\[ 60 = 2(18) + 2W \]

Now, calculate \( 2(18) \):

\[ 60 = 36 + 2W \]

Next, subtract 36 from both sides to isolate the term with \( W \):

\[ 60 - 36 = 2W \]

This simplifies to:

\[ 24 = 2W \]

Now, divide both sides by 2 to solve for \( W \):

\[ W = \frac{24}{2} = 12 \]

Thus, the width of the rectangle is

\[ \boxed{12 \text{ ft}} \]