At Barnes and Noble, Sylvia purchased a journal and a cookbook that cost a total of $54, not including tax. If the price of the journal, j, is $3 more than 2 times the price of the cookbook, c, which system of linear equations could be used to determine the price of each item?
1. The equation for the total cost ____
2. The equation for the price of the journal ___
3. You can choose any method to solve this system: graphing, substitution, or elimination. Choose a method and solve for the price of the journal and the cookbook.
The price of the journal is ___
The price of the cookbook is ____
1. j + c = 54
2. j = 2c + 3
Using substitution:
2c + 3 + c = 54
3c = 51
c = 17
j = 2(17) + 3
j = 37
The price of the journal is $37.
The price of the cookbook is $17.
1. The equation for the total cost: j + c = 54
2. The equation for the price of the journal: j = 2c + 3
To solve this system of equations, we can use the substitution method.
Substitute the value of j from equation 2 into equation 1:
(2c + 3) + c = 54
3c + 3 = 54
Simplify the equation:
3c = 51
Divide both sides by 3:
c = 17
Substitute the value of c into equation 2 to find the value of j:
j = 2(17) + 3
j = 34 + 3
j = 37
The price of the journal is $37,
and the price of the cookbook is $17.
To determine the system of linear equations, let's assign variables to the unknowns in the problem. Let's use 'j' to represent the price of the journal and 'c' to represent the price of the cookbook.
1. The equation for the total cost:
The problem states that the total cost of the journal and the cookbook is $54. Therefore, the equation for the total cost is:
j + c = 54
2. The equation for the price of the journal:
The problem states that the price of the journal, 'j', is $3 more than 2 times the price of the cookbook, 'c'. Therefore, the equation for the price of the journal is:
j = 2c + 3
To solve this system of linear equations, we can use any method - graphing, substitution, or elimination. Let's use the substitution method to solve it.
Substituting the second equation into the first equation, we have:
2c + 3 + c = 54
3c + 3 = 54
3c = 51
c = 17
Now that we have the value for 'c', we can substitute it back into the second equation to find the value of 'j':
j = 2(17) + 3
j = 34 + 3
j = 37
Therefore, the price of the journal is $37, and the price of the cookbook is $17.