1. Samuel is 2/3 as old as his brother. In five years, he will be 3/4 as old as his brother will be. Find their present ages.
a. If x = the brother’s age now, write an expression for Samuel’s present age in terms of x.
b. Write an expression for the brother’s age in five years.
c. Write an expression for Samuel’s age in five years.
d. Write an equation that could be used to solve the problem.
e. Solve the equation, showing each step of your work. Find both Samuel’s present age and his brother’s present age.
f. Check your answer.
2. You can mow your whole lawn in 45 minutes, and your neighbor can mow your whole lawn in 30 minutes. How long would it take you to mow the lawn together? Clearly show and explain each step for full credit.
a.Write an equation that could be used to solve this problem.
b. Solve the equation, showing each step of your work. Find the amount of time it would take to mow the lawn together.
c. Check your answer.
P.S. when you answer it, please let me know what equations or answers go with what letter. and please do the check your answer part and show all work thoroughly. thanks.
a. 2x/3 = Samuel's age.
b. x+5. = Brother's age in 5 yrs.
c. 3/4(x+5) = Samuel's age in 5 yrs.
d.The difference between their ages is the same as it was 5 years ago:
x-2x/3 = (x+5)-3/4(x+5).
e. x-2x/3 = (x+5)-3/4(x+5)
Multiply both sides by 12:
12x-8x = 12x+60-9x-45
4x = 3x+15
4x-3x = 15
X = 15.
2x/3 = 30/3 = 10.
2. Working together is working in parallel:
a. T = (t1*t2)/(t1+t2).
b. T = (45*30)/(45+30) = 18 min.
1. Let's solve the first problem.
a. We are given that Samuel is 2/3 as old as his brother. Let's assume the brother's age is x. Therefore, Samuel's age can be expressed as (2/3) * x.
b. In five years, the brother's age will be x + 5.
c. In five years, Samuel's age will be (2/3) * x + 5.
d. We can write the equation based on the given information:
(2/3) * x + 5 = (3/4) * (x + 5).
e. Let's solve the equation step by step:
Multiply both sides of the equation by 12 to eliminate the fractions:
12 * ((2/3) * x + 5) = 12 * ((3/4) * (x + 5)).
8x + 60 = 9x + 45. (Note: multiplying both sides by 12 causes the denominators to cancel out).
60 - 45 = 9x - 8x (subtract 8x from both sides)
15 = x.
Therefore, the brother's present age is 15 years.
Now, let's calculate Samuel's present age:
Samuel's age = (2/3) * x = (2/3) * 15 = 10 years.
f. To check our answer, let's substitute x = 15 in the equation:
(2/3) * 15 + 5 = (3/4) * (15 + 5).
10 + 5 = (3/4) * 20.
15 = (3/4) * 20.
Both sides are equal, so our answer is correct.
2. Let's solve the second problem.
a. We are given that you can mow the whole lawn in 45 minutes, and your neighbor can mow the whole lawn in 30 minutes. Let's assume the time it would take for both of you to mow the lawn together is y minutes.
b. To calculate the time it would take to mow the lawn together, we can set up the following equation based on the idea that the amount of work done is equal to the rate multiplied by time:
1/45 + 1/30 = 1/y.
Let's find the common denominator and simplify the equation:
(2/90) + (3/90) = 1/y.
5/90 = 1/y.
1/18 = 1/y.
Therefore, y = 18 minutes.
c. To check our answer, let's substitute y = 18 in the equation:
1/45 + 1/30 = 1/18.
(2/90) + (3/90) = 1/18.
5/90 = 1/18.
Both sides are equal, so our answer is correct.