Answer:
lemon = 0
peach = 1
banana = 2
grapes = 3
apple = 4
pear = 5
orange = 6
cherries = 8
strawberry = 9
Explanation:
Let's call the equation lines by numbers. There are 8 equations using fruits.
Let the left column be equations 1, 2, 3, 4, from top to bottom.
Let the right column be equations, 5, 6, 7, 8, from top to bottom.
Look at equation 8.
orange/orange = peach
Since for all integers n, n not zero, n/n = 1, then peach = 1.
Now look at equation 4.
Lemon plus cherries = cherries.
This shows the property of the identity property of zero in addition:
0 + n = n.
Therefore, lemon = 0.
Look at equation 6.
grapes × grapes = strawberry
We are told each fruit represents a 1-digit number.
grapes × grapes does not equal grapes, so grapes cannot be 1.
We can have 2 × 2 = 4 and 3 × 3 = 9 both of which have 1-digit products.
grapes can be only 2 or 3.
strawberry can be only 4 or 9.
Equation 3:
grapes + grapes = orange
orange can be only 4 or 6
Equation 1:
banana + banana + banana = orange
Orange must be a multiple of 3.
Orange must be 6.
3(banana) = orange
3(banana) = 6
banana = 2
Equation 3:
grapes + grapes = orange
2(grapes) = 6
grapes = 3
Equation 6:
grapes × grapes = strawberry
3 × 3 = strawberry
strawberry = 9
Equation 8:
banana-lemon ÷ pear = apple
20 ÷ pear = apple
20 is divisible by 1, 2, 4, 5, 10
We already know what 1 and 2 are. 10 is 2-digit.
pear can only be 4 or 5
apple can only be 4 or 5
Equation 5:
cherries - apple = apple
cherries = 2(apple)
2 × 5 = 10, a 2-digit number, so apple cannot be 5.
apple must be 4
Then pear must be 5.
cherries = 2(apple)
cherries = 8
Answer:
lemon = 0
peach = 1
banana = 2
grapes = 3
apple = 4
pear = 5
orange = 6
cherries = 8
strawberry = 9