Question 309544
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 multi-step word problem.
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Let b = brother's present age
Let s = sister's present age
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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
b + s = 25
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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.
3s - 4b = 5
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Substitution is one way to solve this, rearrange the 1st equation to:
b = (25-s)
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Substitute (25-s) for b in the 2nd equation
3s - 4(25-s) = 5
3s - 100 + 4s = 5
3s + 4s = 5 + 100
7s = 105
s = {{{105/7}}}
s = 15 yrs is sister's age
then using the equation b = 25-s:
b = 25 - 15
b = 10 yrs is brothers age
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Confirm the solution in the 2nd statement;
"four times the brother's age is subtracted from three times the sister's age, the difference is 5."
3(15) - 4(10) = 5
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Do you understand this now???