A container is 1/10 full of grain. If 21 additional gallons of grain are added, the container is 4/5 full. What is the volume of the container, in gallons?
2 answers
Question:
A container is 1/10 full of grain. If 21 additional gallons of grain are added, the container is 4/5 full. What is the volume of the container, in gallons?
Answers
Answer:30 gallonsStep-by-step explanation:let x represent the full container, then[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] xMultiply through by 10 to clear the fractionsx + 210 = 8x ( subtract x from both sides )210 = 7x ( divide both sides by 7 )30 = xThe volume of the container is 30 gallons
Answer: the volume of the container is 30 gallonsStep-by-step explanation:Let V represent the volume of the container, in gallons.The initial volume of grains in the container is 1/0 × V = V/10If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore4/5 × V = 21 + V/104V/5 = 21 + V/104V/5 - V/10 = 217V/10 = 21Multiplying the left hand side and right hand side of the equation by 10, it becomes7V/10 × 5 = 21 × 10 = 2107V = 210V = 210/7 = 30
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