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Cost of 5 egg tarts -> $1.40 × 5 = $7

If price of each piece of cheese cake is $u,

Amount of money Lynn had -> 9u – 9.5 (case 1)

Amount of money Lynn had -> 4u + + 2 (case 2)

9u – 9.5 = 4u + 9

5u = 18.5

u = $3.70

Each piece of cheese cake cost $3.70

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Alternatively, we can make use of the fact that in both cases, 9 items are bought like this…

If Lynn is on a budget and short of $9.50 to buy 9 cheesecakes, she decides to “replace” 5 more expensive cheesecakes with 5 cheaper egg tarts. This way, she saves $9.50+$2=$11.50.

11.50/5=$2.30 –> savings for each replacement of cheesecake with egg tart (egg tart is $1.40 each)

$1.40+$2.30=$3.70# (cost of each cheesecake)

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9 pieces of cheesecake – 9.50 ——- 4 pieces of cheesecake + 5 egg tarts + 2 = 4 pieces of cheesecake and 5 x 1.40 + 2 = 4 pieces of cheesecake + 9
1 piece of cheesecake ——- (9 + 9.50)/ (9 – 4) = 3.70

Ans : $3.70.

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