Question

1. a daycare center expects 20 babies on a given day. how many staff should the center have work that day to maintain a 1/4 ratio (1/4 means 1 to 4 ratio of staff to kids)? (1/4)×20=(x/20)×20 what is the value of x? 2) joe wants 200 euros. the exchange rate is (1.8 dollars)/(1 euro). how many dollars must he give? (1.8 dollars)/(1 euro)=(x dollars)/(200 euros) what is the value of x? 3) a movie has been downloading for 4 minutes and has downloaded 25%. how many minutes are needed for the remaining 75%? (4 min)/(25%)=x/(75%) 4) 0.25 = x/0.75 (4/0.25)×0.75=(x/0.75)×0.75 what is the value of x?

Explanation:

1. For the daycare - staff to kids ratio problem:

• Explanation:
• Step1: Set up the proportion equation
• The ratio of staff to kids is \(\frac{1}{4}\), and there are 20 kids. Let the number of staff be \(x\). The proportion is \(\frac{x}{20}=\frac{1}{4}\).
• Step2: Cross - multiply to solve for \(x\)
• Cross - multiplying gives \(4x = 20\times1\).
• Step3: Solve for \(x\)
• Divide both sides of the equation \(4x=20\) by 4. So \(x=\frac{20}{4}=5\).
• Answer: 5

1. For the currency - exchange problem:

• Explanation:
• Step1: Use the exchange - rate formula
• The exchange rate is 1.8 dollars per 1 euro. Joe wants 200 euros. Let the number of dollars be \(x\). The formula based on the exchange rate is \(\frac{x}{200}=1.8\).
• Step2: Solve for \(x\)
• Multiply both sides of the equation by 200. So \(x = 1.8\times200=360\).
• Answer: 360

1. For the movie - download problem:

• Explanation:
• Step1: Determine the proportion of the download completed and remaining
• 25% of the movie is downloaded, so 75% remains. If 25% took 4 minutes, and let the time for the remaining 75% be \(x\) minutes. Since the rate of download is assumed to be constant, we have the proportion \(\frac{4}{25\%}=\frac{x}{75\%}\).
• Step2: Cross - multiply and solve for \(x\)
• Cross - multiplying gives \(25\%x=4\times75\%\). Since \(25\% = 0.25\) and \(75\%=0.75\), the equation is \(0.25x = 4\times0.75\). Then \(x=\frac{4\times0.75}{0.25}\).
• Step3: Calculate the value of \(x\)
• \(4\times0.75 = 3\), and \(\frac{3}{0.25}=12\).
• Answer: 12

Answer:

1. For the daycare - staff to kids ratio problem:

• Explanation:
• Step1: Set up the proportion equation
• The ratio of staff to kids is \(\frac{1}{4}\), and there are 20 kids. Let the number of staff be \(x\). The proportion is \(\frac{x}{20}=\frac{1}{4}\).
• Step2: Cross - multiply to solve for \(x\)
• Cross - multiplying gives \(4x = 20\times1\).
• Step3: Solve for \(x\)
• Divide both sides of the equation \(4x=20\) by 4. So \(x=\frac{20}{4}=5\).
• Answer: 5

1. For the currency - exchange problem:

• Explanation:
• Step1: Use the exchange - rate formula
• The exchange rate is 1.8 dollars per 1 euro. Joe wants 200 euros. Let the number of dollars be \(x\). The formula based on the exchange rate is \(\frac{x}{200}=1.8\).
• Step2: Solve for \(x\)
• Multiply both sides of the equation by 200. So \(x = 1.8\times200=360\).
• Answer: 360

1. For the movie - download problem:

• Explanation:
• Step1: Determine the proportion of the download completed and remaining
• 25% of the movie is downloaded, so 75% remains. If 25% took 4 minutes, and let the time for the remaining 75% be \(x\) minutes. Since the rate of download is assumed to be constant, we have the proportion \(\frac{4}{25\%}=\frac{x}{75\%}\).
• Step2: Cross - multiply and solve for \(x\)
• Cross - multiplying gives \(25\%x=4\times75\%\). Since \(25\% = 0.25\) and \(75\%=0.75\), the equation is \(0.25x = 4\times0.75\). Then \(x=\frac{4\times0.75}{0.25}\).
• Step3: Calculate the value of \(x\)
• \(4\times0.75 = 3\), and \(\frac{3}{0.25}=12\).
• Answer: 12