Answer: The cost of a single group lesson is $5 and a single private lesson is $25
Step-by-step explanation:
Let the cost of a single group lesson be y.
Let the cost of a single private lesson be z.
A karate school offers a package of 12 group lessons and 2 private lessons for $110. This can be written as:
12y + 2z = 110 ..... equation i
It also offers a package of 10 group lessons and 3 private lessons for $125. This can be written as:
10y + 3z = 125 ...... equation ii
Combining equation i and ii
12y + 2z = 110 ..... equation i
10y + 3z = 125 ...... equation ii
12y + 2z = 110 × (3)
10y + 3z = 125 × (2)
36y + 6z = 330 ....... equation iii
20y + 6z = 250 ...... equation iv
Subtract equation iv from iii
16y = 80
y = 80/16
y = 5
From equation ii
10y + 3z = 125
10(5) + 3z = 125
50 + 3z = 125
3z = 125 - 50
3z = 75
z = 75/3
z = 25
The cost of a single group lesson is $5 and a single private lesson is $25
A group lesson costs = $5.
A private lesson costs = $25.
Let a group lesson costs = $x
A private lesson costs = $y.
According to the question:
12x + 2y = 110
10x + 3y = 125
Solving them we get x = 5, y = 25
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