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.
1. X yrs. = Samuel's bro. age.
2x/3 yrs = Samuel's age.
2x/3 + 5 = 3x/4.
3x/4 - 2x/3 = 5.
Multiply both sides by 12:
9x - 8x = 60
X = 60.
2x/3 = 2*60/3 = 40.
2. T1 = 45 min.
T2 = 30 min.
T=T1*T2 / (T1+T2) = 45*30/(45+30)=18 min
I need a better explanation.. or atleast tell me which answer is for which problem
1. To find the present ages of Samuel and his brother, let's go step by step:
a. Let x be the brother's age now. Since Samuel is 2/3 as old as his brother, his 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 following equation using the given information: (2/3)x + 5 = (3/4)(x + 5).
e. Let's solve the equation step by step:
Start by removing the fractions by multiplying both sides of the equation by 12 (the least common multiple of 3 and 4):
12[(2/3)x + 5] = 12[(3/4)(x + 5)]
Simplifying the left side:
8x + 60 = 9x + 45
Subtracting 8x from both sides:
60 = x + 45
Subtracting 45 from both sides:
15 = x
So, the brother's present age is 15.
Now substitute x = 15 into the expression for Samuel's present age:
Samuel's present age = (2/3)(15) = 10.
Therefore, Samuel is currently 10 years old and his brother is 15 years old.
f. Let's check our answer:
In five years, Samuel's age will be 10 + 5 = 15.
In five years, the brother's age will be 15 + 5 = 20.
And indeed, 15 is 3/4 of 20. So, our answer is correct.
2. To find the time it would take for you and your neighbor to mow the lawn together:
a. Let x be the time it would take for you to mow the lawn together. The equation can be written as follows: 1/45 + 1/30 = 1/x.
b. Let's solve the equation step by step:
Start by finding the least common multiple of 45 and 30, which is 90.
Multiply the equation by 90:
90 * (1/45) + 90 * (1/30) = 90 * (1/x)
Simplifying:
2 + 3 = 90/x
Adding 2 + 3:
5 = 90/x
Now we can find x by dividing both sides of the equation by 5:
x = 90/5 = 18.
Therefore, it would take you and your neighbor 18 minutes to mow the lawn together.
c. Let's check our answer:
Let's see how much of the lawn you and your neighbor can mow in 18 minutes:
In one minute, you can mow 1/45 of the lawn.
In one minute, your neighbor can mow 1/30 of the lawn.
Together, in one minute, you can mow (1/45 + 1/30) of the lawn.
Calculating:
1/45 + 1/30 = 3/90 + 2/90 = 5/90 = 1/18
So, in 18 minutes, you and your neighbor can mow the whole lawn. Our answer is correct.