Question

13. Persevere in solving problems. The cab company runs a promotion on holidays. The flat rate and the fee per mile are the same, but there is a $1 discount off the fare when the distance traveled is greater than 10 miles. a. How can you modify the expression you wrote in Item 12a to represent a holiday cab fare for a distance greater than 10 miles? Explain. b. Lupe's cab fare on a holiday was $7.50. Did Lupe travel more than 10 miles? Justify your answer. C. How many miles did Lupe travel? Manuel's age is twice Gupta's age minus 5. The sum of Manuel's age and Gupta's age is 31. Use this information for Items 14 and 15.Expression of the Item 12, c(m) = 2 + 0.5 • m

Answer 1

$c(m)=2+0.5m$

Where:

c(m) is the cost of the holiday in m miles,

If m greater than 10 there is a discount of $1

So the cost will reduce by $1

$c(m)=2+0.5m-1$

Add the like terms

$c(m)=1+0.5m\text{ , m>10}$

This is the answer of (a)

The cost of the holiday was $7.5, which means

c(m) = 7.5

Let us substitute it in the equation above and find the value of m

$7.5=1+0.5m$

Subtract 1 from both sides

$\begin{gathered} 7.5-1=1-1+0.5m \\ 6.5=0.5m \end{gathered}$

Divide both sides by 0.5 to find m

$\begin{gathered} \frac{6.5}{0.5}=\frac{0.5m}{0.5} \\ 13=m \end{gathered}$

m = 13 which is greater than 10

Lupe travel more than 10 miles

This is the answer of (b)