Grace earns 7 dollars for each car she washes. She always saves 25 dollars of her weekly earnings. This week, she wants to have at least 65 dollars in spending money. How many cars must she wash? Write and solve an inequality to represent this situation. Interpret the solution in context.I know the answer is 12.9< or equal to c, but how do I interpret it? Is it Grace must wash at LEAST 13 cars,or at MOST 13 cars?
7c ≥ 65+25
7c ≥ 90
c ≥ 13
She has to wash at least 13 cars.
To represent this situation, let's define the number of cars Grace needs to wash as "c."
According to the given information, Grace earns 7 dollars for each car she washes. Therefore, Grace's total earnings from washing cars in a week can be represented as: 7c.
It is stated that Grace always saves 25 dollars of her weekly earnings. So, the amount of money Grace has for spending can be represented as: 7c - 25.
Grace wants to have at least 65 dollars in spending money. We can express this as an inequality: 7c - 25 ≥ 65.
To solve this inequality, first, we add 25 to both sides to isolate the term with "c": 7c ≥ 90.
Next, we divide both sides of the inequality by 7 to solve for "c": c ≥ 12.9.
Now let's interpret the solution in context. The inequality c ≥ 12.9 means that Grace must wash at least 13 cars (we round up) to have at least 65 dollars in spending money. Therefore, she needs to wash at least 13 cars in order to meet her spending goal.
To represent this situation with an inequality, we need to determine the total amount of money Grace earns from washing cars. We know that she earns 7 dollars for each car she washes. Let's use 'c' to represent the number of cars she washes.
So the amount of money Grace earns, in dollars, from washing cars is given by 7c.
We also know that Grace saves 25 dollars of her weekly earnings, which means she has (7c - 25) dollars as her spending money.
According to the problem, Grace wants to have at least 65 dollars in spending money. Therefore, we can write the inequality as:
7c - 25 ≥ 65
To solve this inequality, we can add 25 to both sides to isolate the variable:
7c - 25 + 25 ≥ 65 + 25
7c ≥ 90
Finally, divide both sides of the inequality by 7 to solve for c:
c ≥ 90/7
The solution is c ≥ 12.857, which can be rounded to c ≥ 12.9.
When interpreting the solution in context, we need to consider the nature of the variable 'c'. In this case, 'c' represents the number of cars Grace must wash. Since you can't wash a fraction of a car, Grace must wash at least 13 cars, as washing only 12 cars wouldn't guarantee her spending money to be at least 65 dollars. Therefore, the interpretation is that Grace must wash at least 13 cars.