I'm currently struggling a bit here on these 4 math problems. Guidance and solutions are utmost appreciated:
A resort offers vacationers two diving adventure plans. Plan A gives 3 nights lodging and 5 dives. Plan B gives 5 nights lodging and 6 dives.
1) Let n be the number of dollars charged per night and let d be the number of dollars charged per dive. Write 2 expressions, one for the amount you would pay for plan A and the other for the amount you would pay for plan B.
- I asked my teacher for help on this, all the advice she gave was to make two equations so I set:
Amount for lodging = nx
Amount for dives = dy
2) Evaluate the expressions in #1 if lodging is \$125/night and dives are \$50/each. Show the setup.
What I got; not sure if it's right.
- Plan A = 125 x 3 + 50 x 5 = \$650
- Plan B = 125 x 5 + 50 x 6 = \$950
3) If lodging is increased to \$150 per night and dives are decreased to \$35 each, does the cost of either of the plans change? If the cost of a plan changes, does it increase or decrease and by what amount?
Tried this; however, i'm not sure if this is correct.
- Plan A = 150 x 3 + 35 x 5 = \$625
- Plan B = 150 x 5 + 35 x 6 = \$960
Plan A - by \$25 and Plan B + by \$10
4) The resort posts an offer in which plan A costs \$550 and plan B cost \$800. What prices are now being assumed per night and per dive? Show the setup.
Once again, thank you!
4) If we use the definitions in 1) the two equations are
$3n+5d=550 \quad \quad I$
$5n+6d=800 \quad \quad II$
This is a linear equation system with 2 variables and 2 equations. To solve a linear equation system there are 2 methods to solve them: Method of Substitution and Method of Elemination .
I solve the system by using the method of substitution. Solving one equation for one variable. I solve the second equation for $n$
$5n+6d=800$
$5n=800-6d$
Dividing both sides of the equation by 5
$n=160-\frac65 d$
Now we take the expression for $n$ and insert it into the other (first) equation.
$3\cdot (160-\frac65 d) +5d=550$
Multiplying out the brackets
$480-\frac{18}5d+5d=550$
$480-3.6d+5d=550$
$480+1.4d=550$
Subtracting $480$ on both side of the equation
$1.4d=70$
$d=50$
To get the value of n we can use one of the two equations, $I$ or $II$. I use the first one. You can use the second equation and see if you´ll get the same value for $n$.
$3n+5\cdot 50=550$
$3n+250=550$
$3n=300$
$n=100$