Problem of the Week
Problem A and Solution
Fruit Salad
Problem
Robyn needs to buy some fruit for her party. She wants to know the cost of the different fruit.
Each type of fruit has a different price.
Using the above information can you help Robyn determine:
A) How much does one bunch of grapes cost?
B) What is the price of the pineapple?
C) How much does the kiwi cost?
D) Explain how you found the prices.
E) She needs 1 pineapple, 2 bunches of grapes, and 4 kiwis to make her fruit salad. How much
will the ingredients cost?
Solution
A) Since the first picture shows the cost of a pineapple, a kiwi, and grapes, then
if we take away the pineapple and kiwi, we are left with just grapes. Since the
second picture shows the cost of a pineapple and kiwi, then we should take
away 50¢ from the cost of the fruit in the first picture. This means that the
cost of grapes is: $1.00 - 50¢ = 50¢.
B) Since the first picture shows the cost of a pineapple, a kiwi, and grapes, then
if we take away the kiwi and grapes, we are left with just a pineapple. Since
the third picture shows the cost of a kiwi and grapes, then we should take
away 70¢ from the cost of the fruit in the first picture. This means that the
cost of a pineapple is: $1.00 - 70¢ = 30¢.
C) Since we now know the price for a pineapple and grapes, there are a few ways
to calculate the cost of a kiwi. One way is to take a pineapple away from the
second picture. Since a pineapple costs 30¢ then the cost of a kiwi is:
50¢ - 30¢ = 20¢.
Another way is to take the grapes away from the third picture. Since grapes
cost 50¢ then the cost of a kiwi is: 70¢ - 50¢ = 20¢.
D) There are many ways to figure out the prices of each item.
E) Since we have figured out that a pineapple costs 30¢ and a kiwi costs 20¢ and
grapes cost 50¢ we can calculate the cost of the fruit salad as follows:
Cost of the pineapple: 30¢
Cost of the grapes: 2 ⇥ 50¢= $1.00
Cost of the kiwis: 4 ⇥ 20¢ = 80¢
Total cost of the fruit salad: 30¢ + $1.00 + 80¢ = $2.10
Teacher’s Notes
Algebraically, we could solve the problem this way.
Let
Let
Let
For
p represent the cost of one pineapple.
k represent the cost of one kiwi.
g represent the cost of one bunch of grapes.
our equations, we will assume that all of the numbers are cents (¢).
From the first picture diagram we know that:
p + k + g = 100
(equation 1)
From the second picture we know that:
p + k = 50
(equation 2)
From the third picture we know that:
k + g = 70
(equation 3)
Subtract g from both sides of equation 1
p + k + g g = 100 g
p + k = 100 g
(equation 4)
Now the left side of equation 2 equals the left side of equation 4 (both are p + k).
This means the right side of equation 2 must equal the right side of equation 4. So:
50 = 100 g
Now add g to both sides and subtract 50 from both sides
50 + g 50 = 100 g + g 50
g = 50
So a bunch of grapes costs 50¢.
Now, substitute the value of g into equation 3
k + (50) = 70
(equation 5)
And subtract 50 from both sides of equation 5
k + 50 50 = 70 50
k = 20
So a kiwi costs 20¢.
Now, substitute the value of k into equation 2
p + (20) = 50
(equation 6)
And subtract 20 from both sides of equation 6
p + 20 20 = 50 20
p = 30
So a pineapple costs 30¢.