find the value of x and y
x+y=12
45x+52y=561
a sporting goods store sold right hand and left hand batting gloves.12 were sold in a one month period for $561.right handed gloves are $45 and left handed gloves are $52.how many of each were sold? please show work
The equations look fine.
x=12-y
Substitute this term for x in the second equation and solve for y. Put that value in the first equation to find x. Check by putting both values in the second equation.
I hope this helps. Thanks for asking.
x=9
y=3
To find the values of x and y, we can start by using the given equations:
x + y = 12 ...(1)
45x + 52y = 561 ...(2)
We can rearrange equation (1) to solve for x by subtracting y from both sides:
x = 12 - y
Now, substitute this value of x into equation (2):
45(12 - y) + 52y = 561
Distribute 45 to simplify:
540 - 45y + 52y = 561
Combine like terms:
7y = 561 - 540
7y = 21
Divide both sides by 7 to solve for y:
y = 3
Now substitute this value of y back into equation (1) to solve for x:
x + 3 = 12
x = 12 - 3
x = 9
So, we have found that x = 9 and y = 3. This means that 9 right-handed gloves and 3 left-handed gloves were sold.
To check if these values are correct, substitute x = 9 and y = 3 into equation (2):
45(9) + 52(3) = 405 + 156 = 561
Since the left side of equation (2) equals the right side, we have confirmed that our values for x and y are correct.
Therefore, 9 right-handed gloves and 3 left-handed gloves were sold.