MATH QUESTION (HARD)

Question

if abby gives $10 to ben,then they will have the same amount of money. if ben gives $20 to abby, then shell have four times the amount of ben. how much money do each of them have in the start? (MATH QUESTION)

Answer 1

Thanks for your question!

This problem has two variables. Well use "a" for Abby and "b" for Ben.

The first sentence tells us if Abby gives $10 to Ben, they will have the same amount of money. We can write this as:

a = b +10

Second, if Ben gives $20 to Abby, then she will have 4 times the amount of Ben. We can write this as:

a + 20 = 4b

OR

(a+20)/4 = b

I'm going to use this final equation to substitute the value of b in the first equation.

Now we have:

a = (a+20)/4 + 10

This gets rid of the "b" variable and lets us work on finding "a".

From here we can plug in values into the equation and see if they are true.

Say you try a=10

a = (a+20)/4 + 10

10 = (10+20)/4 + 10

10 = 30/4 + 10

10 = 7.5 + 10

10 = 17.5

This is not true. "a" must not be 10.

Say you try a=20

a = (a+20)/4 + 10

20 = (20+20)/4 + 10

20 = 40/4 + 10

20 = 10 + 10

20 = 20

This is true! Now we know a = 20.

Recall the first equation: a = b +10

If we plug in 20 in for "a," we can simplify to get b = 10.

Finally, we can check our work by plugging in our answers to the second problem:

a + 20 = 4b (a = 20; b = 10)

20 + 20 = 4(10)

40 = 40

This is true! We have solved the problem!

I hope this helped!