Mal bought 3 bottles of milk and 4 bags of chips for a total of $17. At the same shop, Barbara bought 1 bottle of milk and 5 bags of chips for $13.
Find how much each bottle of milk and each bag of chips cost by completing the following steps:
a) Define two variables to represent the problem.
b) Write a pair of simultaneous equations relating to the two variables.
c) Solve the pair of equations using substitution or elimination.
d) Write your answer in words.
For me, I only know how to answer a) and b) which is:
a) Let $m be the milk, Let $c be the chips
b) 3m + 4c = 17
m + 5c = 13
one comment, on b: you need to be specific $m is bottles of milk, $c is bags of chips.
c. 3m + 4c = 17
m + 5c = 13
multiply second equation by -3, then add the equations.
4c-15c=17-3*12
solve for c. then put c into either equation, and solve for m
c) To solve the pair of equations, we can use either substitution or elimination method. Here, we will use the elimination method.
Let's multiply the second equation by 3 to make the coefficient of 'm' the same as the first equation:
3(m + 5c) = 3(13)
3m + 15c = 39
Now, we can subtract the first equation from the second equation to eliminate 'm':
(3m + 15c) - (3m + 4c) = 39 - 17
11c = 22
Divide both sides of the equation by 11 to solve for 'c':
11c/11 = 22/11
c = 2
Now substitute the value of 'c' back into either of the original equations, let's use the first equation:
3m + 4(2) = 17
3m + 8 = 17
3m = 9
m = 3
So, each bottle of milk costs $3 and each bag of chips costs $2.
d) Each bottle of milk costs $3 and each bag of chips costs $2.
c) To solve the pair of equations, we can use the method of substitution. Step-by-step instructions for solving the equations using substitution are as follows:
1. Start with the first equation: 3m + 4c = 17.
2. Solve this equation for one variable (in terms of the other variable). Let's solve for m:
3m = 17 - 4c.
Divide both sides of the equation by 3:
m = (17 - 4c) / 3.
3. Now substitute the expression for m into the second equation: m + 5c = 13.
Replace m with the expression derived in step 2:
(17 - 4c) / 3 + 5c = 13.
4. Simplify and solve for c:
Multiply both sides of the equation by 3 to get rid of the fraction:
17 - 4c + 15c = 39.
Combine like terms:
11c = 22.
Divide both sides by 11 to solve for c:
c = 2.
5. Now substitute the value of c back into either of the original equations to solve for m. Let's use the first equation:
3m + 4(2) = 17.
3m + 8 = 17.
3m = 9.
Divide both sides by 3 to solve for m:
m = 3.
d) Therefore, each bottle of milk (m) costs $3, and each bag of chips (c) costs $2.