When buying gasoline, you notice that 14 gallons of gasoline is approximately the same as 53 liters. Use this information to find a linear model that relates gallons to liters. Then use the model to find the number of liters in 25 gallons. Round your answer to the nearest tenth.
If x is liters and y is gallons, then
y = kx
k = 14/53
now plug in y=25
Or, since the ratio is always the same, and you have
(25/14) as many gallons, you will have
(25/14) * 53 liters
To find a linear model that relates gallons to liters, we can set up a proportion based on the given information.
We know that 14 gallons is approximately the same as 53 liters. Let's set up the proportion:
14 gallons / 53 liters = x gallons / y liters
Assuming x represents the number of gallons and y represents the number of liters, we can solve for y by cross-multiplying:
14 gallons * y liters = 53 liters * x gallons
14y = 53x
Now we have a linear equation that relates gallons (x) to liters (y).
To find the number of liters in 25 gallons, we can substitute x = 25 into the equation and solve for y:
14y = 53(25)
14y = 1325
y = 1325 / 14
y ≈ 94.6
Therefore, there are approximately 94.6 liters in 25 gallons.