Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Peter is renting two kinds of rafts for a vacation company. One type seats 3
people and the other seats 5 people. If 53 people are using the vacation
company and he rents 13 rafts, how many of each type of raft does he rent?

Sagot :

LanceLongFei

Answer:

Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Step-by-step explanation:

Let [tex]x[/tex] denote the number of rafts seating 3 people and [tex]y[/tex] the number of rafts seating 5 people. The total number of rafts is 13, so [tex]x+y=13[/tex]. We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so [tex]3x+5y=53[/tex].

It's always a good idea to put these equations under each other:

[tex]\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.[/tex]

We can subtract the first equation three times from the second one to obtain [tex](3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7[/tex]

Now, substitute this found value for [tex]y[/tex] into [tex]x+y = 13[/tex] and we see that [tex]x=6[/tex]. We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.