Question

Multistep word problems Word problems are more complicated with two or more unknown values. First, assign a variable to each unknown value. The word problem should then be translated into the appropriate number of mathematical equations, which can then be solved by substitution. Keep in mind that the number of mathematical equations needed is equal to the number of variables.Consider the following multistep word problem: The sum of the ages of a brother and sister is 25. If four times the brother's age is subtracted from three times the sister's age, the difference is 5.Consider just the first sentence of this multistep word problem. Sentence 1: The sum of the ages of a brother and sister is 25.Give an equation that represents this statement using as the age of the brother and as the age of the sister ??????If four times the brother's age is subtracted from three times the sister's age, the difference is 5.Give an equation that represents this statement using b as the age of the brother and s as the age of the sister.

Answer 1

The age of the brother is 10 and the age of the sister is 15.

Explanation:

Firstly, we want the first equation where:

b = Brother's age

s = Sister's age

So the equation is:
`b+s = 25`

The second equation is four times the brother's age is subtracted from three times the sister's age, the difference is 5. Therefore, we get:

`3s - 4b = 5`

Now, we've got a system of equations. when we can use the substitution method (or any other method) to get the value of the variables.

From equation 1
`b+s=25\\b = 25 - s`

And now substitute to eq. 2

`3s - 4(25-s)  = 5\\3s - 100 + 4s = 5\\7s = 105\\s = (105)/(7) \\s = 15`

Therefore:

`b+15=25\\b=25-15\\b=10`