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

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.

⇒
`(x)/(y) = (9)/(5)`

By cross multiply, we have;

5x = 9y

Divide both sides by 5 we get;

`x = (9)/(5)y`

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

`(9)/(5)y + y = 98`

Combine like terms;

`(14)/(5)y = 98`

Multiply both sides by
`(5)/(14)` we get;

`y =98 * (5)/(14) = 7 * 5 = 35`

Substitute the value of y= 35 in
`x = (9)/(5)y` to solve for x;

`x = (9)/(5) * 35 = 9 * 7 = 63`

(a)

System of linear equation that represents situation is:

`x + y = 98`

`x = (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.