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Matthew has 35 dollars more than his friend. If they have 100 dollars all together. w much does Matthew have?

Matthew has $35$ dollars more than his friend. If they have $100$ dollars all together. w much does Matthew have?

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Time and work rate problems

Full solution

Q. Matthew has

35

dollars more than his friend. If they have

100

dollars all together. w much does Matthew have?

Set Up Equations: Let's call the amount of money Matthew's friend has $F$ dollars. $\newline$ Then Matthew has $F + 35$ dollars. $\newline$ Together, they have $F + (F + 35) = 100$ dollars.
Solve for F: Now we solve for F: $\newline$ $2F + 35 = 100$ $\newline$ $2F = 100 - 35$ $\newline$ $2F = 65$
Find $F$ : Divide both sides by $2$ to find $F$ : $F = \frac{65}{2}$ $F = 32.5$
Calculate Matthew's Amount: Now we find out how much Matthew has: $\newline$ Matthew has $F + 35$ dollars. $\newline$ Matthew has $32.5 + 35$ dollars. $\newline$ Matthew has $67.5$ dollars.

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