Dear Sir
I need help for the below questions
Please help
thanks
larry King
1) Sally bought some erasers and pens 16.50. She bought 5 fewer erasers than pens. Each erasers cost $1.80 more than the pen. How many pens did she buy?
2. A group of people met at a party. Each person shook hands with everyone else. John shook hands with 3 times as many men as women. Jane shook hands with 4 times as many men as women. How many men and how many women were there at the party?
Dear Larry,
I would be happy to help you with your questions. Let's break down each question one by one and explain how to arrive at the answers.
1) Sally bought some erasers and pens for $16.50. She bought 5 fewer erasers than pens, and each eraser cost $1.80 more than a pen. We need to find out how many pens she bought.
To solve this problem, we can set up equations based on the information given. Let's assume the number of pens Sally bought is x. Since she bought 5 fewer erasers than pens, the number of erasers she bought would be (x - 5).
Now, we know that the total cost of the pens and erasers is $16.50. Each pen costs p dollars, and each eraser costs (p + $1.80) dollars. Therefore, the equation would be:
x * p + (x - 5) * (p + $1.80) = $16.50
Simplifying this equation will give us the value of x, which represents the number of pens Sally bought.
2) A group of people met at a party, and each person shook hands with everyone else. John shook hands with 3 times as many men as women, and Jane shook hands with 4 times as many men as women. We need to find out how many men and how many women were at the party.
To solve this problem, let's assume the number of men is m, and the number of women is w.
According to the information given, John shook hands with 3 times as many men as women, so he shook hands with 3w men. Jane shook hands with 4 times as many men as women, so she shook hands with 4w men.
Now, if we sum up the number of handshakes between John and Jane with that of the remaining people, it should be equal to the total number of handshakes in the group. The total number of handshakes in a group can be calculated using the formula: (n * (n - 1)) / 2, where n represents the number of people.
So, the equation for the total number of handshakes would be:
(m + w) * (m + w - 1) / 2 = (3w + 4w) + ((m + w - 2) * (m + w - 1) / 2)
Simplifying this equation will give us the values of m and w.
I hope this explanation helps you understand how to approach and solve these problems. If you have any further questions, feel free to ask!
Best regards,
Explain Bot