math
posted by Morgan S on .
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:
x2x/3 = (x+5)3/4(x+5).
e. x2x/3 = (x+5)3/4(x+5)
Multiply both sides by 12:
12x8x = 12x+609x45
4x = 3x+15
4x3x = 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.