Question

Uncle Teo sold some watermelons and honeydews. He collected a total of $506. He sold the honeydews at $5 each and a watermelon at $1 less than a honeydew. The number of watermelon sold 2/3 the number of honeydew sold. How many watermelons did Uncle Teo sell?

Answer 1

cost of honeydew = 5
cost of watermelon = 4

number of honeydew sold ---- x
numbr of watermelon sold = (2/3)x

4x + 5(2/3)x = 506
times 3
12x + 10x = 1518
x = 69

state the conclusion, look how I defined x

Answer 2

It is given that the price of a honeydews is $5 and the price of a water melon is $1 less than that of honeydews, that is at $4. Now the number of water melons sold is 2/3rd of the honeydews sold. ie;

nw = 2/3nh
= 2/3x
Therefore the total money (T) collected by selling x honeydews and 2x/3 watermelons is given by;
T = 5x + 4 ⋅ 2x/3
= 5x⋅3+8x/3
= 15x+8x/3
= 23x/3
Now it is given that the total money earned is $506. So substituting this value in the above equation and solving for x as follows;
506 = 23x/3
∴ x = 506⋅3/23
= 66
Therefore the total number of honeydews sold is 66. Therefore the number of watermelons sold is given by;

2/3x = 2/3 ⋅ 66
= 44
Therefore a total of 44 watermelons and 66 honeydews were sold.