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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:
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.
⇒[tex]x + y = 98[/tex] ......[1]
Also, it is given that the ratio of food tents to retails tents is 9 : 5.
⇒ [tex]\frac{x}{y} = \frac{9}{5}[/tex]
By cross multiply, we have;
5x = 9y
Divide both sides by 5 we get;
[tex]x = \frac{9}{5}y[/tex]
Substitute this value x in equation [1] to solve for y;
[tex]\frac{9}{5}y + y = 98[/tex]
Combine like terms;
[tex]\frac{14}{5}y = 98[/tex]
Multiply both sides by [tex]\frac{5}{14}[/tex] we get;
[tex]y =98 \times \frac{5}{14} = 7 \times 5 = 35[/tex]
Substitute the value of y= 35 in [tex]x = \frac{9}{5}y[/tex] to solve for x;
[tex]x = \frac{9}{5} \times 35 = 9 \times 7 = 63[/tex]
(a)
System of linear equation that represents situation is:
[tex]x + y = 98[/tex]
[tex]x = \frac{9}{5}y[/tex]
(b)
As x represents the food tents.
Therefore, 63 food tents are at the market.
(c)
y= 35 retail tents are at the market.