2) Write a word problem using the information from the given equation and inequality. Be sure to include all seven parts and an appropriate question requesting a solution for the unknown (variable).
The seven parts of a one-variable equation are as follows:
1 – correct variable term for the left side expression
2 – correct constant term for the left side expression
3 – correct operation between the terms of the left side expression
4 – correct equal sign or inequality symbol
5 – correct variable term for the right side expression
6 – correct constant term for the right side expression
7 – correct operation between the terms of the right side expression
Inequality: 58x + 170 > 42x + 320
1 – correct variable term for the left side expression: 58x
2 – correct constant term for the left side expression: 170
3 – correct operation between the terms of the left side expression: +
4 – correct equal sign or inequality symbol: >
5 – correct variable term for the right side expression: 42x
6 – correct constant term for the right side expression: 320
7 – correct operation between the terms of the right side expression: +
Word problem:
Mary has a savings account. She currently has $170 in her account. Every month, she deposits $58 into her account. On the other hand, she has expenses of $320 per month. Her income from a side job is represented by the variable x.
Question: How many months does Mary need to work her side job (represented by the variable x) for her savings account to have more money than her expenses account?
To solve the problem, we can set up the inequality:
58x + 170 > 42x + 320
This inequality represents the condition that Mary's savings account with the amount saved (58x + 170) should be greater than her expenses account (42x + 320). By finding the value of x that satisfies this inequality, we can determine the number of months needed for Mary to have more money in her savings account than in her expenses account.