answer:Let's denote the number of blue crayons as B. Since there are four times as many red crayons as blue crayons, the number of red crayons will be 4B. The total number of crayons in the box is the sum of the blue crayons and the red crayons, which is given as 15. So we can write the equation: B + 4B = 15 Combining like terms, we get: 5B = 15 Now, to find the number of blue crayons (B), we divide both sides of the equation by 5: 5B / 5 = 15 / 5 B = 3 So, there are boxed{3} blue crayons in the box.

answer:He already had 157 liters of paint and needed to buy 176 more liters. To find out the total amount of paint he wanted to use, you add the two amounts together: 157 liters + 176 liters = 333 liters So, he wanted to use a total of boxed{333} liters of paint for his project.

answer:To solve this problem, we start by translating the given information into mathematical equations. We are given two conditions: 1. When the wood is measured with the rope, there are 4.5 feet of rope left over. This means the rope is longer than the wood by 4.5 feet. We can express this as: [y = x + 4.5] 2. When the rope is folded in half and used to measure the wood again, there is 1 foot of wood left. This means half the length of the rope is 1 foot shorter than the wood. We can express this as: [frac{1}{2}y = x - 1] From these two conditions, we can form the system of equations: [left{begin{array}{l} y = x + 4.5 frac{1}{2}y = x - 1 end{array}right.] This system of equations matches option A: [boxed{A: left{begin{array}{l} y = x + 4.5 frac{1}{2}y = x - 1 end{array}right.}] **Explanation:** - The first equation comes from the fact that the entire length of the rope exceeds the length of the wood by 4.5 feet. - The second equation is derived from the scenario where the rope is folded in half, indicating that half of the rope's length is 1 foot less than the wood's length. **Review:** This question tests our ability to abstract real-world problems into systems of linear equations. Understanding the relationships between the lengths of the wood and the rope is crucial for setting up the correct equations.

answer:To find the volume of a rectangular box with given areas of its faces, we use the dimensions l, w, and h to represent the length, width, and height of the box, respectively. The volume of the box is given by the formula V = lwh. Given that the areas of the faces are 24 square inches, 16 square inches, and 6 square inches, we can set up the following equations based on the areas of the rectangular faces: 1. lw = 24 2. wh = 16 3. lh = 6 To find the volume, we need to solve for lwh. By multiplying all three equations together, we get: [l^2w^2h^2 = 24 cdot 16 cdot 6] This simplifies to: [l^2w^2h^2 = 2^3 cdot 3 cdot 2^4 cdot 2 cdot 3] Further simplification gives: [l^2w^2h^2 = 2^8 cdot 3^2] To find lwh, we take the square root of both sides: [lwh = sqrt{2^8 cdot 3^2}] [lwh = 2^4 cdot 3] [lwh = 16 cdot 3] [lwh = 48] Therefore, the volume of the rectangular box is boxed{48} cubic inches.