Question

Q10 The sale price S (in dollars) of an item is given by the formula S=L−rL
, where L
is the list price (in dollars) and r
is the percent of discount (in decimal form).

Solve the formula for r
.

The list price of the shirt is $21.50. What is the percent of discount?





Q11 You and your friend drive toward each other. The equation 50h=190−45h
represents the number h
of hours until you and your friend meet. After how many hours will you meet?
Q12 Solve the inequality

4−2m>7−3m
Q13 Graph the inequality

x>2





Q14 The altitude a
(in feet) of a plane t
minutes after takeoff is given by a=3400t+600
. How many minutes after takeoff is the plane at an altitude of 21,000 feet?

Explain step by step pls

Answer 1

Sure! Let's solve each question step-by-step.

### Q10

**Problem**: The formula for the sale price \( S \) of an item is given by:

\[
S = L - rL
\]

We need to solve the formula for \( r \) and then find the percent of discount when the list price \( L \) is $21.50.

**Step 1**: Rearrange the formula to isolate \( r \).

\[
S = L - rL
\]

This can be rewritten as:

\[
S = L(1 - r)
\]

Now, to isolate \( r \), we can divide both sides by \( L \):

\[
\frac{S}{L} = 1 - r
\]

Now, subtract 1 from both sides:

\[
\frac{S}{L} - 1 = -r
\]

Multiply both sides by -1:

\[
r = 1 - \frac{S}{L}
\]

**Step 2**: Calculate \( r \) using the values for \( L \) and \( S \).

We don't have \( S \) given directly, but we can define it as \( S = L - \text{(discount)} \):

If \( S = L(1 - r) \), and for a discount to be figured, let’s say if for example the shirt was sold for \( S = $15 \) (you can replace this with your actual sale price).

Given that \( L = 21.50 \):

\[
r = 1 - \frac{S}{L}
\]

Inserting the values (assuming hypothetical sale price as $15):

\[
r = 1 - \frac{15}{21.50}
\]
\[
r = 1 - 0.6977 \approx 0.3023
\]

To express \( r \) as a percentage:

\[
\text{percent of discount} = r \times 100 \approx 30.23\%
\]

### Q11

**Problem**: Solve the equation

\[
50h = 190 - 45h
\]

**Step 1**: Combine like terms by adding \( 45h \) to both sides:

\[
50h + 45h = 190
\]

This simplifies to:

\[
95h = 190
\]

**Step 2**: Divide both sides by 95 to solve for \( h \):

\[
h = \frac{190}{95} = 2
\]

**Conclusion**: You will meet after 2 hours.

### Q12

**Problem**: Solve the inequality

\[
4 - 2m > 7 - 3m
\]

**Step 1**: Add \( 3m \) to both sides:

\[
4 - 2m + 3m > 7
\]

This simplifies to:

\[
4 + m > 7
\]

**Step 2**: Subtract 4 from both sides:

\[
m > 3
\]

### Q13

**Problem**: Graph the inequality

\[
x > 2
\]

**Step 1**: On a number line, locate 2.

**Step 2**: Draw an open circle at 2 (indicating that 2 is not included in the solution) and shade everything to the right of 2, indicating all numbers greater than 2.

### Q14

**Problem**: The altitude \( a \) of a plane is given by:

\[
a = 3400t + 600
\]

We need to find \( t \) when \( a = 21000 \).

**Step 1**: Set up the equation:

\[
21000 = 3400t + 600
\]

**Step 2**: Subtract 600 from both sides:

\[
21000 - 600 = 3400t
\]
\[
20400 = 3400t
\]

**Step 3**: Divide by 3400 to isolate \( t \):

\[
t = \frac{20400}{3400}
\]
\[
t = 6
\]

**Conclusion**: The plane reaches an altitude of 21,000 feet 6 minutes after takeoff.

Let me know if you need any more details or further assistance!