Academy sports equipment store is having a sale on bike helmets and water bottles. one bike club purchased 10 helmets and 2 water bottles for 155$. Another bike club purchased 12 bike helmets and 3 water bottles for 189$. Write a system of linear equations to determine the price for an adult and the price for a child. Solve the equation
Let's denote the price of an adult bike helmet as "A" and the price of a child bike helmet as "C." We can also denote the price of a water bottle as "W."
According to the given information, the first bike club purchased 10 helmets and 2 water bottles for $155. We can write the following equation for this bike club:
10A + 2W = 155
Similarly, the second bike club purchased 12 helmets and 3 water bottles for $189. We can write the following equation for this bike club:
12A + 3W = 189
We now have a system of linear equations:
10A + 2W = 155 (1)
12A + 3W = 189 (2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiplying equation (1) by 3 and equation (2) by 2, we have:
30A + 6W = 465 (3)
24A + 6W = 378 (4)
Subtracting equation (4) from equation (3), we get:
30A + 6W - (24A + 6W) = 465 - 378
6A = 87
A = 87/6
A ≈ 14.50
Substituting the value of A back into equation (1), we can solve for W:
10(14.50) + 2W = 155
145 + 2W = 155
2W = 155 - 145
2W = 10
W = 10/2
W = 5
Therefore, the price of an adult bike helmet is approximately $14.50, and the price of a child bike helmet is approximately $5.