Question

The farmer's market has a total of 98 tents.  the ratio of food tents to retail tents is 9:5. a. Write a system of linear equations that represent this situation. b.  How many food tents are at the market? c. How many retail tents are at the market?

Answer 1

F+r=98
5f=9r
F is food tents, r is retail tents.
Plug in f=9/5r to the top to get 14/5r=98. Then 2/5r=14. So r=35 and f=9/5*35=63.

Answer 2

Answer:

Let x represents the food tents and y represents the retail rents.

As per the given statement: The farmer's market has a total of 98 tents.

⇒$x + y = 98$                    ......[1]

Also, it is given that the ratio of food tents to retails tents is 9 : 5.

⇒ $\frac{x}{y} = \frac{9}{5}$

By cross multiply, we have;

5x = 9y

Divide both sides by 5 we get;

$x = \frac{9}{5}y$

Substitute this value x in equation [1] to solve for y;

$\frac{9}{5}y + y = 98$

Combine like terms;

$\frac{14}{5}y = 98$

Multiply both sides by $\frac{5}{14}$ we get;

$y =98 \times \frac{5}{14} = 7 \times 5 = 35$

Substitute the value of y= 35 in $x = \frac{9}{5}y$ to solve for x;

$x = \frac{9}{5} \times 35 = 9 \times 7 = 63$

(a)

System of linear equation that represents situation is:

$x + y = 98$

$x = \frac{9}{5}y$

(b)

As x represents the food tents.

Therefore, 63 food tents are at the market.

(c)

y= 35 retail tents are at the market.