Write a real-world problem that you can model with the two-step equation 5x + 7 = 10. Then solve the problem.
Real-world problem: Suppose you have a bakery that sells cookies. You want to find out how many batches of cookies you need to bake in order to have a total of 10 cookies ready for sale. Each batch of cookies you bake yields 5 cookies, and you already have 7 cookies available.
Solution:
Let x be the number of batches of cookies to bake.
The equation representing the problem is 5x + 7 = 10.
To solve the equation:
1. Subtract 7 from both sides of the equation:
5x = 10 - 7
5x = 3
2. Divide both sides of the equation by 5:
x = 3/5
Therefore, you need to bake 3/5 of a batch of cookies to reach a total of 10 cookies for sale.
A real-world problem that can be modeled with the two-step equation 5x + 7 = 10 is finding out how many apples (x) a person can buy if each apple costs $5 and the person has $10 to spend.
To solve the problem, we need to isolate the variable (x) and find its value.
Step 1: Subtract 7 from both sides of the equation.
5x + 7 - 7 = 10 - 7
5x = 3
Step 2: Divide both sides of the equation by 5 to get the value of x.
5x/5 = 3/5
x = 3/5
Therefore, the person can buy 3/5 of an apple with $10, which is equivalent to approximately 0.6 of an apple.
Sure! Let's say the problem involves finding the number of hours (represented by x) it would take to earn enough money to buy a new video game console.
We can model this problem using the equation 5x + 7 = 10, where 5x represents the amount of money earned per hour, 7 represents the initial amount of money already saved, and 10 represents the total amount needed to buy the video game console.
To solve this two-step equation, we need to isolate the variable x, which represents the number of hours needed to earn the required amount of money.
Here's how we can solve it step by step:
Step 1: Subtract 7 from both sides of the equation to isolate the term with x:
5x + 7 - 7 = 10 - 7
5x = 3
Step 2: Divide both sides of the equation by 5 to solve for x:
5x/5 = 3/5
x = 3/5
Therefore, it would take approximately 3/5 of an hour (or 36 minutes) to earn enough money to buy the video game console.