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
To solve, we can use substitution:
Substitute the second equation into the first:
(2c + 3) + c = 54
Simplify:
3c + 3 = 54
Subtract 3 from both sides:
3c = 51
Divide both sides by 3:
c = 17
Now we can use this value to find j:
j = 2c + 3 = 2(17) + 3 = 37
Therefore, the price of the journal is $37 and the price of the cookbook is $17.
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+Response area.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel: y = 18 + 4x
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel: y = 18 + 4x
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
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 linear equations, I'll use substitution.
Substituting the value of j from equation 2 into equation 1:
(2c + 3) + c = 54
Combining like terms:
3c + 3 = 54
Subtracting 3 from both sides:
3c = 51
Dividing both sides by 3:
c = 17
Now, we can substitute the value of c back into equation 2 to find j:
j = 2(17) + 3
j = 34 + 3
j = 37
So, the price of the journal is $37 and the price of the cookbook is $17.
To solve this problem, let's first define our variables:
Let j be the price of the journal.
Let c be the price of the cookbook.
We are given that the price of the journal, j, is $3 more than two times the price of the cookbook, c. We can write this information as an equation:
j = 2c + 3 ----(equation 1)
We are also given that the total cost of the journal and cookbook together is $54. This can be represented by the equation:
j + c = 54 ----(equation 2)
Now we have a system of two linear equations consisting of equation 1 and equation 2. We can solve this system using any of the three methods: graphing, substitution, or elimination.
Let's solve it using the elimination method:
1. Multiply equation 1 by -1 to change the sign of the equation:
-1(j) = -1(2c + 3)
-j = -2c - 3 ----(equation 3)
2. Add equation 2 and equation 3:
(j + c) + (-j) = 54 + (-2c - 3)
The j term cancels out, leaving us with:
c - 2c - 3 = 54 - 3
Simplifying this, we get:
-c - 3 = 51
-c = 51 + 3
-c = 54
Multiplying through by -1 to isolate c, we get:
c = -54
Now that we have the value of c, we can substitute it back into equation 1 to find the value of j:
j = 2c + 3
j = 2(-54) + 3
j = -108 + 3
j = -105
Therefore, the price of the journal is $-105 (which doesn't make sense in this context) and the price of the cookbook is $-54.
However, it seems like there might be an error in the problem statement as negative prices are not realistic.