Assess which explanation on how to obtain the value of x in the equation 4/x=36/81 is reasonable.(1 point)
Responses
Reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.
Reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.
Divide 81 by 9 to obtain the value of x.
Divide 81 by 9 to obtain the value of x .
Divide 36 by 81, and then multiply by 4 to determine the value of x.
Divide 36 by 81, and then multiply by 4 to determine the value of x .
Multiply the numerators and denominators. Equate the product to calculate the value of x.
The reasonable explanation to obtain the value of x in the equation 4/x=36/81 would be to reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.
A vehicle requires 12 of a liter of gasoline to cover a distance of 7.5 kilometers (km). What distance can be covered with 2 liters?(1 point)
Responses
48 km
48 km
60 km
60 km
15 km
15 km
30 km
To find the distance that can be covered with 2 liters of gasoline, we can set up a proportion:
Liters of Gasoline / Distance = 12 liters / 7.5 km
Simplifying the proportion:
2 liters / Distance = 12 liters / 7.5 km
Cross-multiplying:
2 liters * 7.5 km = 12 liters * Distance
15 km = 12 liters * Distance
Dividing both sides of the equation by 12 liters:
15 km / 12 liters = Distance
Distance = 1.25 km
Therefore, the distance that can be covered with 2 liters of gasoline is 1.25 km.
To obtain the value of x in the equation 4/x = 36/81, we need to find a reasonable explanation.
The first two explanations are identical, which is reducing the second ratio by dividing both numbers by 9, and then multiplying the result by 4. This method is reasonable because it allows us to simplify the equation and solve for x.
The third explanation suggests dividing 36 by 81 and then multiplying by 4 to determine the value of x. This method is not reasonable because dividing 36 by 81 does not involve x and will not lead to an accurate solution.
The fourth explanation suggests multiplying the numerators and denominators and equating the product to calculate the value of x. This method is also not reasonable because it does not take into account the fact that the equation involves division and not multiplication.
Therefore, the reasonable explanation is to reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.