what is a word problem for 2x-4=8?
You baked two pans of cookies. Your brother ate four of these cookies and now you have 8 left.
How many cookies were on each pan to begin with?
2x-4=8
+4 +4
2x=12
x=6
Sure! Here's a word problem that can be represented by the equation 2x - 4 = 8:
"Sam has twice as many pens as his friend Matt. The total number of pens they have together is 8 more than four times the number of pens Sam has. How many pens does each of them have?"
Let's solve this problem step-by-step:
Step 1: Let's assign variables to the unknowns.
- Let x represent the number of pens Sam has.
- Since Matt has half the number of pens as Sam, let's assign the variable y to represent the number of pens Matt has.
Step 2: Write an equation based on the given information.
- Sam has twice as many pens as Matt: x = 2y
- The total number of pens they have together is 8 more than four times the number of pens Sam has: x + y = 4x + 8
Step 3: Substitute the value of x from the first equation into the second equation.
- Substituting x with 2y in the second equation: 2y + y = 4(2y) + 8
Step 4: Simplify the equation.
- Combining like terms: 3y = 8y + 8
Step 5: Solve for y.
- Subtracting 8y from both sides: 3y - 8y = 8
- Simplifying: -5y = 8
- Dividing by -5: y = -8/5 or -1.6
Step 6: Calculate x using the value of y.
- Since x = 2y, substituting y with -1.6: x = 2(-1.6) = -3.2
Step 7: Verify the solution.
- Plug in the values of x and y into the original equations to check if they satisfy both equations.
Therefore, the solution to the word problem is that Sam has -3.2 pens (which is not possible) and Matt has -1.6 pens (also not possible). Hence, there is no valid solution for this particular word problem.
A word problem that corresponds to the equation 2x - 4 = 8 can be formulated as follows:
"Sarah is saving money to buy a new bicycle. She currently has $4 saved up. Her goal is to save twice as much money as she currently has. If each week she saves $2, how many weeks will it take her to reach her savings goal?"
To solve this word problem, we need to translate it into an equation using the given information.
Let's define the number of weeks Sarah saves as "x". We know that each week she saves $2, so the amount of money she saves after "x" weeks is 2x.
According to the problem, Sarah's goal is to have twice the amount of money she currently has, which is $4. Therefore, her savings goal is 2 times $4, which is $8.
We can now set up the equation:
2x - 4 = 8
To find the number of weeks it will take for Sarah to reach her goal, we solve this equation for "x".