A vegetable store sold 3 tons of vegetables less on the first day than on the second- and on the third day it sold 5-9 of the amount sold in the first two days- How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days-

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Solving a Quadratic Equation by Factorization Method

A vegetable s...

Question

A vegetable store sold $3$ $t o n s$ of vegetables less on the first day than on the second, and on the third day it sold $\frac{5}{9}$ of the amount sold in the first two days.
How many vegetables was the store selling every day if it sold altogether $98$ $t o n s$ of vegetables for the three days?

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Solution

Step-1: Finding the equation for all three days:
Assume that the amount of vegetables sold on the second day is $x$
On first day, amount of vegetables sold $= x - 3$
On second day, amount of vegetables sold $= x$
On third day, amount of vegetables sold $= \frac{5}{9} (x + x - 3)$
Total amount of vegetables sold $= 98$ $tons$
Step-2: Finding the value of $x$
$∴ (x - 3) + x + \frac{5}{9} (2 x - 3) = 98 \Rightarrow (\frac{10}{9} + 2) x - \frac{14}{3} = 98 \Rightarrow \frac{28 x - 42}{9} = 98 \Rightarrow 28 x = 98 \times 9 + 42 \Rightarrow x = \frac{924}{28} \Rightarrow x = 33 tons$
Step-3: Finding the amount of vegetables sold each day
On first day, amount of vegetables sold $= 33 - 3$
$= 30$ $t o n s$
On second day, amount of vegetables sold $= 33$ $t o n s$
On third day, amount of vegetables sold $= \frac{5}{9} (33 + 33 - 3)$
$= 35$ $t o n s$
Hence, the amount of vegetables sold on first, second and third day is $30$ $t o n s$ , $33$ $t o n s$ and $35$ $t o n s$ .

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A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 59 of the amount sold in the first two days. How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days?