would you please check my work and make changes for errors? thanks ann
problem: joe bought 3- topping sundae for 15.25 and a 5 topping sundae for 17.75.
write and solve a system of linear equations to find price of each topping and a plain sundae(no toppings).
I wrote:
x + 5y = 17.75
-x+ -3y= 15.25
2y = 2.50
y = 1.25 price per topping
x = 15.25 - 3(1.25)
x = 15.25 - 3.75
x = 11.50 price per plain sundae
To check your work and make changes, let's go step by step through your solution:
1. First, let's write down the equations correctly based on the given information:
Let x be the price of a plain sundae (no toppings).
Let y be the price of each topping.
The first equation should represent the 5-topping sundae:
5y + x = 17.75
The second equation should represent the 3-topping sundae:
3y + x = 15.25
2. Now, let's solve the system of equations. We can use the method of elimination or substitution. Let's use the method of elimination by subtracting the second equation from the first equation:
(5y + x) - (3y + x) = 17.75 - 15.25
5y - 3y + x - x = 2.50
2y = 2.50
So, your equation 2y = 2.50 is correct.
3. Now, let's solve for y:
2y = 2.50
Divide both sides of the equation by 2:
y = 2.50 / 2
y = 1.25
So, your solution for the price per topping (y) is correct. It is $1.25.
4. Finally, let's solve for x using either of the original equations. Let's use the second equation:
3y + x = 15.25
Substitute the value of y as 1.25:
3(1.25) + x = 15.25
3.75 + x = 15.25
Subtract 3.75 from both sides of the equation:
x = 15.25 - 3.75
x = 11.50
So, your solution for the price per plain sundae (x) is correct. It is $11.50.
To summarize, your solutions for the price per topping (y) and the price per plain sundae (x) are both correct. The price per topping is $1.25, and the price per plain sundae is $11.50.