Video Transcript
Charlotte has two 𝑥 plus seven
dollars. She gives three 𝑦 minus two
dollars to Benjamin and then receives 𝑥 minus 𝑦 dollars from Jacob. Write a simplified expression for
the remaining amount of money, in dollars, that Charlotte has.
We first note that the amount of
dollars that Charlotte has will be the amount she starts with minus the amount she
gives away plus the amount she receives. She starts with two 𝑥 plus seven
dollars. She gives away three 𝑦 minus two
dollars, so we need to subtract this. She then receives 𝑥 minus 𝑦
dollars, so we need to add this. Our expression is two 𝑥 plus seven
minus three 𝑦 minus two plus 𝑥 minus 𝑦.
Next, we need to collect the like
terms. Two 𝑥 plus 𝑥 is equal to three
𝑥. Negative three 𝑦 plus negative 𝑦
is the same as negative three 𝑦 minus 𝑦, which equals negative four 𝑦. Finally, seven minus negative two
is the same as seven plus two, which equals nine.
Our expression therefore simplifies
to three 𝑥 minus four 𝑦 plus nine. This is the total number of dollars
that Charlotte now has.
