Sandra had twice as many apples as oranges at first. She removed 4 apples and 3 oranges each time. In the end, there were 18 apples and 1 orange left. How many fruits did Sandra have at first?
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My solution:
Let 1u be the number of times Sandra “removed 4 apples and 3 oranges”
. _______4u_______ ____18___
. / \/ \
A |--------------|--------------|
O |--------------|
. \____ ___/\ / \____ ___/\ /
. 3u 1 3u 1
From the model above,
4u + 18 = 6u + 2
or
16 = 2u
1u = 16/2 = 8
Number of fruits at the start:
7u + 19 = 7x8 + 19 = 56 + 19 = 75
or
(3u+1)x3 = (3x8+1)x3 = 25 x 3 = 75
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Alternative (Simpler):
Redrawing the above model for the Apple Branch by dividing “4u+18” to two “2u+9” :
. __2u_ _9___ __2u_ _9___
. / \/ \ / \/ \
A |--------------|--------------|
O |--------------|
. \____ ___/\ /
. 3u 1
3u-2u = 9-1
1u = 8
Number of fruits at the start:
(2u + 9) x 3 = ( 2x8 + 9)x3 = 25 x 3 = 75
or
(3u+1)x3 = (3x8+1)x3 = 25 x 3 = 75
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