the cost of 2 bottles of water and 3 pretzels is $16.50 whereas 4 bottles of water and 1 pretzel is $15.50. Find the cost of a water bottle and a pretzel.
per " bottle of water "= $3.00
per " pretzels" = 3.50
2x3.00=6
3x3.50= 10.50
you add them together you get 16.50
for the second part
4x3=12
1x3.50=3.50
you add them together you get 15.50
2w + 3p = 16.50
4w+p = 15.50
double the first:
4w+6p = 33
4w + p = 15.50
subtract them
5p = 17.50
p = 3.50
into the original 2nd:
4w + 3.50 = 15.50
4w = 12
w = 3.00
Water costs $3.00 per bottle, and $3.50 per pretzel
To find the cost of a water bottle and a pretzel, we can set up a system of equations based on the given information. Let's assume the cost of a water bottle is represented by 'w' and the cost of a pretzel is represented by 'p'.
From the first statement, "the cost of 2 bottles of water and 3 pretzels is $16.50," we can write the equation:
2w + 3p = 16.50 ----(1)
From the second statement, "4 bottles of water and 1 pretzel is $15.50," we can write another equation:
4w + 1p = 15.50 ----(2)
Now we have a system of equations:
2w + 3p = 16.50
4w + 1p = 15.50
To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation (1), we can isolate 'w' in terms of 'p':
2w = 16.50 - 3p
w = (16.50 - 3p) / 2 ----(3)
Now, substitute equation (3) into equation (2):
4[(16.50 - 3p) / 2] + p = 15.50
Multiply both sides of the equation by 2 to eliminate the fraction:
4(16.50 - 3p) + 2p = 31
Expand and simplify:
66 - 12p + 2p = 31
-10p = 31 - 66
-10p = -35
Divide both sides by -10 to solve for 'p':
p = -35 / -10
p = 3.50
Now substitute the value of 'p' back into equation (3) to find 'w':
w = (16.50 - 3(3.50)) / 2
w = (16.50 - 10.50) / 2
w = 6 / 2
w = 3
Therefore, the cost of a water bottle is $3 and the cost of a pretzel is $3.50.
Per "Bottles of water"=$2.50
Per "Pretzels" =$3.00