Let's Play Baseball

Let $x$ be the cost of the baseball.

Because the bat cost $100 more than the baseball, so the bat cost $(x + 100)$ .

And sum of their cost is given to be $110.

Converting the statement above to an equation, we get $x + (x+ 100) = 110$ .

Simplifying it and solve it: $2x+ 100 = 110 \quad\Rightarrow\quad 2x = 10 \quad\Rightarrow\quad x= 5$ .

Since $x = 5$ , and $x$ denote the cost of the baseball, then the cost of the ball is $5.

We're told that the Bat + Ball = $110, which can be rewritten as

Bat = $110 - Ball

We're also told that the bat costs $100 more than the ball, so we can write

Bat = $100 + Ball

Because Bat = $110 - Ball and Bat = $100 + Ball, we can set the two right hand sides equal to each other to obtain

$110 - Ball = $100 + Ball $\longrightarrow$ 2(Ball) = $10

If two balls together cost $10, then one ball costs $5.

Let ${x}$ = cost of ball (in $) then: $x + (100+x) = 110 \Rightarrow\ x=5$

A logical question, the only way to satisfy the problem is the ball costing $5 and the bat $105. Then, $5 + $105 = $110.

suppose, baseball=x and bat=x+100

so, $x+x+100=110$

or, $2x=10$

or, $x=5$ ..............[the cost of baseball]

Let x =cost of the ball, then x+x+100=110 2x=10 therefore,x=5

Let $b_1 = Bat$ and $b_2 = Ball$

From the question we can gather that

$b_1 + b_2 = 110$

$b_1 = b_2 + 100$

Substituting the second equation into the first one gives

$(b_2 + 100) + b_2 = 110$

Expand the brackets to get

$2b_2 + 100 = 110$

Re-arrange the equation to get a value for $b_2$

$2b_2 + 100 = 110 \Rightarrow 2b_2 = 110 - 100 \Rightarrow 2b_2 = 10 \Rightarrow b_2 = 5$

So the ball costs $5$ $

Let the cost of bat be $ x It is given that the cost of bat is $100 more than the cost of ball Therefore the cost of ball = x+10 Total cost of bat and ball = $110 Cost of ball = x+x+100 = 110 Cost of ball = 2x+100 = 110 Cost of ball = 2x = 110 - 100 Cost of ball = 2x=10 Cost of ball = x = 10 divided by 2 Cost of ball = x = 5 Therefore cost of ball = $5

That is again simple simultaneous equations and much easier to solve than the Twizzlers and M&Ms, but still simpler we used to solve it by another method which always worked. I would leave the decision to experts whether it is valid or not.

We take away the figure of 100 from the total amount which leaves us with 10. We divide 10 by 2 to get 5. Now if we add 100 to one value it will become 105 while other will be 5. Thus satisfying both conditions.

This always works for the simplest linear simultaneous equations (sum of two numbers x and y is a and difference is b). Another way to reach the answer is add a and b and divide the sum by 2 which in essence is canceling the simultaneous equations and removing one variable. You can also start by taking the difference of a and b and dividing it by 2 to get the other figure and then work the other one out by simple addition or subtraction.

There is another more logical method which will work for any two simultaneous linear equations.

I will first explain the principle then use it to solve this example. 1. Take one condition first (e.g. sum of the prices). 2. Give an arbitrary value to price of ball (or bat, it will make no difference). 3. Work out the price of bat. 4. Work out the difference between the price of bat and ball. If it satisfies the second condition there you are. If not then becomes the next bit and now pay attention. 5. Change the price of ball by an arbitrary figure say 1. 6. Repeat steps 3 and 4. 7. See how much and in what direction it changes the value obtained in step 4. As for this example increasing the price of ball by 1 will reduce the original difference by 2. 8. Work out how much you need to increase or decrease the price of the ball so that the difference comes down to 100. Now let us work it out. 1. Price of ball 0. Price of bat 110. Difference 110. 2. Raise the price by 1. Price of ball 1. Price of bat 109. Difference 108. 3. Raising the price by 1 reduces the difference by 2. 4. We need to reduce the difference by a further 8 to bring it to 100 (or a total of 10 from the original assumption). 5. Now simple arithmetic will tell that we need to increase the price of ball by $4 to bring the difference to 100 thus making it $5. It will also work if you start with the second condition i.e. the difference being 100 with any arbitrary value of ball and then going through the same steps to bring the sum to 110.

It always works with linear equations and obviates the need for algebra and geometry

Let's call the bat is $a$ & the ball is $b$ .Using $\frac{(a+b)-(a-b)}{2}=\frac{a+b-a+b}{2}=\frac{2b}{2}=b$

So the answer is $\frac{(110-100)\$}{2}=\frac{10\$}{2}=\boxed{\large{5\$}}$

let cost of ball be 'a '.according to given condition,cost of bat+cost of ball=110 also given that bat costs 100 more than ball,i.e 100+a+a=110 i.e 100+2a=110 hence , a=5,which is the cost of ball... .

2ball+100=110

ball=(110-100)/2

ball=5

let x=baseball and y=bat so, x+y=110 ........( 1 ) but the question says'' the bat costs $100 more than the ball.'' so, y=x+100.......(2) put the value of y from the equation of( 2) into the equation of( 1)... x+x+100=110 from this , x=5 as x=ball so the ball costs $5. Thank you..

let the cost of ball be x . therefore, cost of bat= $100+x => $100+x+x = $110 => x = 5$