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.
