I am 5% older than my wife.my wife is x% younger then i am.Find x???
Well, it seems like you're trying to figure out the percentage difference between you and your wife's ages. If you're 5% older than your wife, that means you could say you're 105% of her age. Since your wife is x% younger than you, we could say she is 100% - x% of your age. So, combining these two, we have:
Your age = 105% of your wife's age
Your wife's age = (100% - x%) of your age
Now, we need to find x. Let's put these two equations together:
105% of your wife's age = (100% - x%) of your age
But hey, let's have some fun with this! How about a joke instead? Why don't scientists trust atoms anymore?
Because they make up everything!
Let's solve for x based on the given information. We know that you are 5% older than your wife. This means that your age, let's call it Y, is 105% of your wife's age.
Mathematically, we can write this equation as:
Y = 1.05 * W,
where Y represents your age and W represents your wife's age.
We also know that your wife is x% younger than you. This means that her age, let's call it Z, is (100 - x)% of your age.
Mathematically, we can write this equation as:
Z = (100 - x)% * Y,
where Z represents your wife's age.
Now, let's substitute the value of Y from the first equation into the second equation:
Z = (100 - x)% * (1.05 * W).
Since Z represents your wife's age and W represents your wife's age, we can substitute Z with W in the equation:
W = (100 - x)% * (1.05 * W).
Now let's simplify the equation:
W = (100 - x) * 1.05 * W.
Divide both sides by W to solve for x:
1 = (100 - x) * 1.05.
Divide both sides by 1.05:
1 / 1.05 = 100 - x.
1.05 / 1.05 = 100 - x / 1.05.
0.9524 = 100 - x.
Subtract 100 from both sides:
0.9524 - 100 = -x.
-99.0476 = -x.
Now divide both sides by -1 to get x:
x = 99.0476.
Therefore, x is approximately 99.0476%.
To find the value of x, we need to use the information given. Let's break it down step by step:
1. You are 5% older than your wife. This means that your age is equal to 105% of your wife's age.
2. Your wife is x% younger than you. This means that her age is equal to (100 - x)% of your age.
To solve for x, we can set up an equation using the information from steps 1 and 2:
Your age = 105% of your wife's age
Your age = 1.05 * wife's age
Wife's age = (100 - x)% of your age
Wife's age = (100 - x)/100 * your age
Since your age and your wife's age are equal, we can set the two equations equal to each other:
1.05 * wife's age = (100 - x)/100 * your age
Now, we can solve for x by isolating it on one side of the equation:
1.05 * wife's age = (100 - x)/100 * (1.05 * wife's age) (we substituted your age with 1.05 * wife's age)
1.05 * wife's age = (100 - x)/100 * 1.05 * wife's age
Divide both sides of the equation by 1.05 * wife's age:
1 = (100 - x)/100
Multiply both sides of the equation by 100:
100 = 100 - x
Simplifying the equation:
x = 0
Therefore, x is 0.
It you are 1.05 times you wife's age, your wife is 1/1.05 = 0.95238 times your age. That makes her 4.7619% younger than you
x = 4.7619