Question

The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.

Answer 1

Answer:

Option C is correct.

$A = 2\frac{3}{4}$ miles.

Step-by-step explanation:

Find the missing quantities in a ratio table where a total is given,

first determine the unit rate from the ratio of two given quantities and use it to find the missing quantities in each equivalent ratio.

Find the constant rate;

We can  use the row that gives both quantities, not the total.

$\frac{7}{3\frac{1}{2} } = \frac{7}{\frac{7}{2} } =\frac{7 \times 2}{7} = 2$

Now, we write the equation of relationship:

$B'= 2R$ where B' is the distance Biked (in miles) and R is the distance Run(miles)

To find the missing value of A;

using above relationship;

$5\frac{1}{2} =2 \times A$

$\frac{11}{2} = 2A$

Divide both sides by 2 we get;

$\frac{11}{2 \times 2} =A$

Simplify:

$A =\frac{11}{4} = 2\frac{3}{4}$ miles.

Similarly; find the missing value of B;

Using above relationship;

$B = 2 \times 2\frac{1}{8} = 2 \times \frac{17}{8}$

Simplify:

$B = \frac{17}{4} =4\frac{1}{4}$

Therefore, the value of $A=2\frac{3}{4}$ miles.