Answer :
14.54 tons of grapes are needed for 7850 bottles.
Step-by-step explanation:
Given,
4320 bottles of wine = 8 tons of grapes
1 bottle of wine = [tex]\frac{8}{4320}[/tex]
1 bottle of wine = [tex]\frac{1}{540}[/tex]
Expected demand = 7850 bottles
7850 bottles = x tons of grapes
[tex]x= 7850*\frac{1}{540}\\x=\frac{7850}{540}\\x=14.54[/tex]
14.54 tons of grapes are needed for 7850 bottles.
Keywords: fractions, multiplication
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To produce 7850 bottles of wine, the winery will need approximately 14.56 tons of grapes.
First, we need to determine the ratio of the number of bottles produced to the tons of grapes used in the initial year. The winery produced 4320 bottles of wine from 8 tons of grapes, so the ratio is[tex]:\[ \text{Ratio} = \frac{\text{Bottles produced}}{\text{Tons of grapes}} = \frac{4320}{8} \]This ratio simplifies to:\[ \text{Ratio} = \frac{540}{1} \][/tex]
This means that for every ton of grapes, the winery can produce 540 bottles of wine. Next year, the winery expects the demand to reach 7850 bottles. To find out how many tons of grapes are needed to produce this amount, we use the ratio we calculated:[tex][ \text{Tons of grapes needed} = \frac{\text{Expected bottles}}{\text{Ratio}} = \frac{7850}{540} \]Now, we perform the division:\[ \text{Tons of grapes needed} = \frac{7850}{540} \approx 14.537037037 \][/tex]Since it's not practical to have a fraction of a ton of grapes, the winery would likely round up to ensure they have enough grapes to meet the demand. Therefore, they will need approximately 14.56 tons of grapes, rounding to two decimal places for precision.
