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?

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.

Answered by avtrisal | 2024-06-10

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.
⇒ y x ​ = 5 9 ​
By cross multiply, we have;
5x = 9y
Divide both sides by 5 we get;
x = 5 9 ​ y
Substitute this value x in equation [1] to solve for y;
5 9 ​ y + y = 98
Combine like terms;
5 14 ​ y = 98
Multiply both sides by 14 5 ​ we get;
y = 98 × 14 5 ​ = 7 × 5 = 35
Substitute the value of y= 35 in x = 5 9 ​ y to solve for x;
x = 5 9 ​ × 35 = 9 × 7 = 63
(a)
System of linear equation that represents situation is:
x + y = 98
x = 5 9 ​ 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. ;

Answered by OrethaWilkison | 2024-06-24

The system of equations for the farmer's market is x + y = 98 and 5 x = 9 y . There are 63 food tents and 35 retail tents at the market. This was determined by solving the equations simultaneously.
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Answered by OrethaWilkison | 2024-09-27