Gustavs father is seven times as olda s he is.a. Year ago,he was nine timesa s olda s gustav. Find gustavs present age
g = Gustavs age
f = Fathers age
Gustavs father is 7 times as olda s he is.
f = 7 g
Year ago,he was nine timesa s olda s gustav
( f - 1 ) / ( g - 1 ) = 9
( 7 g - 1 ) / ( g - 1 ) = 9 Multiply both sides by ( g - 1 )
7 g - 1 = 9 ( g - 1 )
7 g - 1 = 9 g - 9 Subtract 7 g to both sides
7 g - 1 - 7 g = 9 g - 9 - 7 g
- 1 = 2 g - 9 Add 9 to both sides
- 1 + 9 = 2 g - 9 + 9
8 = 2 g Divide both sides by 2
4 = g
g = 4
f = father
g = Gustav
Write two equations.
f = 7g
f - 1 = 9(g - 1)
Substitute first equation into second.
7g - 1 = 9g - 9
7g - 9g -1 + 1 = 9g - 9g - 9 + 1
-2g = -8
-2g/-2 = -8/-2
g = 4
Substitute g value in either equation.
f = 7(4)
f = 28
Check:
One year ago.....
f is 27 and 9 times older than g
g is 3
27 = 3 * 9
Gustav -- x
his father -- 7x
One year ago:
Gustav -- x-1
his father -- 7x-1
7x-1 = 9(x-1)
7x-1 = 9x - 9
-2x = -8
x = 4
Gustav is now 4 years old
check:
his father is now 28
one year ago, Gustav was 3 and his father would have been 27, which is 9 time Gustav's age
If 22.5 L of nitrogen at 748 mm Hg are composed of 725 mm Hg at constant. What is yhe new volume?
To find Gustav's present age, let's assign variables to the unknowns.
Let's say Gustav's present age is represented by the variable 'G', and his father's present age is represented by the variable 'F'.
From the information given, we know that Gustav's father is seven times as old as Gustav: F = 7G.
It is also mentioned that a year ago, Gustav's father was nine times as old as Gustav: F - 1 = 9(G - 1).
Now we can solve these equations simultaneously to find the value of 'G'.
First, substitute the value of F from the first equation into the second equation:
7G - 1 = 9(G - 1).
Let's solve this equation:
7G - 1 = 9G - 9.
Bring the variables on one side and the constants on the other side:
7G - 9G = -9 + 1.
-2G = -8.
Divide both sides by -2:
G = -8 / -2.
G = 4.
Therefore, Gustav's present age is 4 years.