#1
Mr. Jones got a loan for a sum of money, and at the time of repayment he owed $75 in interest. Mr. Brown borrowed three times the amount of money Mr. Jones had borrowed at the same rate of interest for twice as long a time. How much interest does Mr. Brown pay?
#2
Mr. Baker earns $448 a week. He spends 86% of this amount for expenses. The amount he saves in a year of 52 weeks is.
#3
In a high school there are 768 pupils. Of these, 3/8 are girls. If 5/6 of the girls are below the senior class, the number of senior girls is.
#4
Last month, Nate spent 12% of his paycheck on car repairs and 25% of the remainder on food. He gave $1320 of the remaining money to his parents and then bought a computer on sale. If the usual price of the computer was $825 and the discount was 20%, how much money did Nate have in the beginning?
#1
To find out how much interest Mr. Brown pays, we first need to determine the amount of money he borrowed. We can do this by finding the amount Mr. Jones borrowed and then multiplying it by three.
Since Mr. Jones owed $75 in interest at the time of repayment, we can assume this is the total interest paid over the entire loan duration. To find the amount he borrowed, we need to subtract the interest from the total amount owed.
Let's represent the amount Mr. Jones borrowed as "x." Therefore, the total amount Mr. Jones owed can be expressed as "x + $75."
Since Mr. Brown borrowed three times the amount Mr. Jones borrowed, we can represent the amount Mr. Brown borrowed as "3x."
Now, let's find out the loan duration for Mr. Brown. It is mentioned that Mr. Brown borrowed for twice as long as Mr. Jones did. So, if Mr. Jones borrowed for "t" time units, Mr. Brown borrowed for "2t" time units.
In order to calculate the interest paid by Mr. Brown, we need to use the formula:
Interest = Principal * Rate * Time
Since the rate is the same for Mr. Jones and Mr. Brown, we don't need to consider it. Let's calculate the interest paid by Mr. Brown.
Interest paid by Mr. Brown = (Principal borrowed by Mr. Brown) * (Loan duration of Mr. Brown)
= (3x) * (2t)
Therefore, the amount of interest paid by Mr. Brown will be 6 times the interest paid by Mr. Jones, assuming the loan duration and interest rate are the same.
#2
To find the amount Mr. Baker saves in a year, we first need to calculate the expenses he incurs weekly. We can do this by finding 86% of his income.
Let's represent Mr. Baker's income as "I." Therefore, his weekly expenses can be calculated as 86% of his income, which can be expressed as: Expenses = 0.86 * I.
Since Mr. Baker saves the remaining amount after expenses, we can calculate his savings per week: Savings = Income - Expenses.
To find the annual savings, we need to multiply the weekly savings by 52 (the number of weeks in a year).
Annual savings = Weekly savings * 52
#3
To find the number of senior girls in high school, we first need to determine the total number of girls in the school. We can do this by multiplying the total number of students by the fraction representing the proportion of girls in the school.
Let's represent the total number of students in the high school as "T" and the fraction of girls as "G." Therefore, the total number of girls can be calculated as: Number of girls = T * G.
Since 3/8 of the girls are below the senior class, we can represent this fraction as "3/8 * G." Therefore, the number of senior girls can be calculated as: Number of senior girls = Number of girls - (3/8 * Number of girls).
#4
To find out how much money Nate had in the beginning, we need to perform a series of calculations.
First, let's assume Nate's paycheck is represented by "P".
Nate spent 12% of his paycheck on car repairs, so the amount remaining is (100% - 12%) of his paycheck.
Next, Nate spent 25% of the remainder on food, which means he has (100% - 25%) of the remaining amount remaining.
Now, Nate gave $1320 of the remaining money to his parents. Therefore, he has the remaining amount minus $1320.
Finally, Nate bought a computer on sale. The sale price of the computer was 20% less than the usual price. Therefore, the amount he spent on the computer is 80% of the computer's usual price.
By calculating all these deductions and subtractions, we can determine the amount of money Nate had in the beginning.
Just translate the words to algebra. Then solve. For example,
#3:
3/8 of 768 = 288
5/6 are below senior, so 1/6 are seniors.
1/6 of 288 = 48
Where do you get stuck on the others?