Explain how you got the answer! I need help solving system equations !

Question

marisol sold cookie dough containers, boxes of soft pretzels, and pasta packages as part of a fundraiser for avid. Cookie dough sold for $7.50 per container, boxes of soft pretzels sold for $25, and the pasta sold for $6.25 per packages. Marisol raised $925. She noticed the number of boxes of soft pretzels she sold was three times the number of containers of cookie dough. The number of packages of pasta plus 4 was the same as the number of boxes of soft pretzels minus the number of containers of cookie dough.

How many of each type of item did marisol sell during the fundraiser?

Answer 1

Let's call the number of cookie dough sold c. Each is sold for $7.50

Let's call the number of boxes of soft pretzel sold, s. Each is sold for $25

Let's call the number of pasta sold, p. Each is sold for $6.25

Money made selling cookie dough is c*$7.50

Money made selling soft pretzel is s*$25

Money made selling pasta is p*$6.25

Total money made is 7.50*c+25*s+6.25*p = 925

She noticed the number of boxes of soft pretzels she sold was three times the number of containers of cookie dough -> s = 3*c

The number of packages of pasta plus 4 was the same as the number of boxes of soft pretzels minus the number of containers of cookie dough. -> (p+4) = (s-c)

Now that we have three equations ans three unknowns (p,s, and c), we can solve this problem.

Substitute, s=3c, in p+4 = s-c => p+4 = 3c-c => p+4 = 2c => p=2c-4

Substitute s=3c and p=2c-4 in 7.50*c+25*s+6.25*p = 925

7.5c + 25 (3c) + 6.25 (2c-4) = 925

7.5c + 75c + 12.5c - 25 = 925 . Now combine all c terms

95c - 25 = 925. Now move all constants to one side (right side in this case)

95c = 925+25 = 950

c = 950/95 = 10 boxes of cookie dough

Substitute c=10 in s = 3c => s = 3*10 = 30 boxes of soft pretzel

Substitute c=10 in p=2c-4 => p = 2*10 - 4 = 16 boxes of pasta

Let's check our answer=>

7.50*c+25*s+6.25*p = 7.5*10+25*30+6.25*16 = 75+750+100 = 925 Check!

Answer 2

X is the cookie dough

Y is the pretzels

Z is the pasta

7.5X + 25y + 6.25z = 925

y = 3x

y-x = z+4

3x - x = z+4

2x = z+4

2x-4 = z

7.5x + 25(3x) + 6.25(2x-4) = 925

7.5x + 75x + 12.5x - 25 = 925

95x = 950

x=10

z = 16

y = 30