Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and he earns money each Saturday morning at his grandmother’s store. Write an inequality for the amount of money Carlos will need to earn each Saturday morning, and describe the solutions. Assume Carlos will earn the same amount each Saturday morning.

Question

Carlos must earn at least $__ each Saturday morning to have at least $200 in four weeks.

Answer 1

To determine how much Carlos needs to earn each Saturday morning, we start with the information provided:

1. Carlos needs at least $200 after four weeks.
2. His mom gives him $30.
3. He will earn money every Saturday morning at his grandmother’s store for 4 Saturdays.

Let \( x \) be the amount Carlos earns each Saturday. Over four weeks, Carlos will earn \( 4x \).

Now, we can set up the inequality to express Carlos's total savings after four weeks:

\[ 30 + 4x \geq 200 \]

Next, we will solve this inequality to find out how much Carlos needs to earn each Saturday.

1. Subtract 30 from both sides:

\[ 4x \geq 200 - 30 \] \[ 4x \geq 170 \]

2. Now, divide both sides by 4:

\[ x \geq \frac{170}{4} \] \[ x \geq 42.5 \]

This means Carlos must earn at least $42.50 each Saturday morning.

Conclusion

Carlos must earn at least $42.50 each Saturday morning to have at least $200 in four weeks.

Description of the Solutions

The solutions to this inequality are all values of \( x \) such that \( x \geq 42.5 \). This means that if he earns $42.50 or more on each of the four Saturdays, he will reach his goal of having at least $200. Any amount above $42.50 will also satisfy the goal.

Answer 2

Jerrica is packing a box that can hold at most 65 pounds. She starts by putting a container in the box that weighs 26 pounds. She plans to fill the rest of the box with books. Each book she places in the box weighs 1.3 pounds. Write an inequality for the number of books Jerrica can put in the box, and describe the solutions.
__x+__ ≤__ , where x is the number of books Jerrica can put in the box. Jerrica can put at most __ books in the box.

Answer 3

To determine how many books Jerrica can put in the box, we can set up an inequality based on the situation described.

1. The maximum weight the box can hold is 65 pounds.
2. Jerrica puts in a container that weighs 26 pounds.
3. Each book weighs 1.3 pounds.

Let \( x \) be the number of books Jerrica can put in the box. The total weight of the books will be \( 1.3x \) pounds.

The inequality that describes the total weight in the box is:

\[ 26 + 1.3x \leq 65 \]

Now, let’s solve this inequality to find out how many books she can fit in the box:

1. Subtract 26 from both sides:

\[ 1.3x \leq 65 - 26 \] \[ 1.3x \leq 39 \]

2. Now, divide both sides by 1.3:

\[ x \leq \frac{39}{1.3} \] \[ x \leq 30 \]

Conclusion

The inequality can be written as:

\[ 1.3x + 26 \leq 65 \]

This shows that the weight of the books plus the weight of the container cannot exceed 65 pounds.

Jerrica can put at most 30 books in the box.

Description of the Solutions

The solutions to this inequality are all integer values of \( x \) such that \( x \leq 30 \). This means Jerrica can put 0 up to 30 books in the box, and any amount within that range will satisfy the condition of not exceeding the weight limit.