Question 402002
Write an equation for each statement, simplify each equation:
:
"A is eleven times as old as B."
a = 11b
:
"In a certain number of years A will be five times as old as B,"; y = no. of yrs
a + y = 5(b+y)
a + y = 5b + 5y
a = 5b + 5y - y
a = 5b + 4y
replace a with 11b
11b = 5b + 4y
11b - 5b = 4y
6b = 4y
6b - 4y = 0
:
"five years after that she will be three times as old as B." That's y+5 yrs
a + y + 5 = 3(b + y + 5)
a + y + 5 = 3b + 3y + 15
a = 3b + 3y - y + 15 - 5
a = 3b + 2y + 10
replace a with 11b
11b = 3b + 2y + 10
11b - 3b = 2y + 10
8b = 2y + 10
8b - 2y = 10
:
Multiply above equation by -2, add to the 1st equation
-16b + 4y = -20
 6b - 4y = 0
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-10b = -20
b = 2 yrs old
Find a
a = 11(2)
a = 22 yrs old
:
We can say their present ages are: A=22; B=2
:
:
To check our our solutions, Find y
6(2) - 4y = 0
12 - 4y = 0
-4y = -12
y = 3 yrs is that "certain number of years"
;
Check in the statement:
"In a certain number of years A will be five times as old as B,
22 + 3 = 5(2 + 3)
25 = 25
:
You can check the solutions in the 3rd statement:
"five years after that she will be three times as old as B." That's y+5 yrs"