Solve each word problem, using two different variables . Remember to delcare you

Question

Solve each word problem, using two different variables. Remember to delcare your varibales, make and label a picture or a chart when ever possible, show the equations ,and state your answer in a sentence.

1) An airline that flies from Los Angeles to Albuquerque with a stopover in Phoenix charges a fare of $90 to Phoenix and a fare of $120 from Los Angeles to Albuquerque. A total of 185 passengers boarded the plane in Los Angeles, and fares totaled $21,000. How many passengers got off in Phoenix?

2) A large table for a conference room is to be constructed in the shape of a rectangle with to semicircles at the ends. The table's perimeter of 40 feet, and the area of the rectangle portion is to be twice the sum of the areas of the two ends. Find the length and width of the rectangle portion of the table.

(something like this)

3) A silversmith has two alloys, one containing 35% silver and the other 60% silver. How much of each should be melted and combined to obtain 100 grams of an alloy containing 50% silver?

4) A man rows a boat 500 feet upstream against the constant current in 10 minutes. He then rows 300 feet downstream (with the same current) in 5 minutes. Find the speed of the current and the rate at which he can row in still water.

( plz use "add/edit custom equation and add/edit custion diagram" if u want to or u know how to use it) Thanks!

Explanation / Answer

1. let x = number of people who paid $90 to fly to phoenix let y = number of people who paid $120 to fly to albuquerque x+y=185 and $90x+$120y=$21000 therefore x = 185-y substitution yields $90(185-y)+$120y=$21000 solve yeilds y=145 then x = 40 2. this question is missing some information but it's solved the same way as below let L = length of the rectangle table, W = width of the rectangle table and r = radius of the semi circles at the ends. P = perimeter of the table = 40 = 2L+2(pi)r Area rectangle = 2(area of the 2 semicricle) = (2(area of a full circle) = 2(pi*r^2) therefore 2(pi)r = 40-2L substitution Area rectangle = LW = 2(pi)r*r = (40-2L)*r solve for W = (40r-2Lr)/L 3. let x = grams of alloy with .35 silver let y = frams of alloy with .60 silver x+y=100 and .35x+.60y=.50 therefore x = 100-y substitution yields .35(100-y)+.60y=.50 solve yeilds y=60 then x = 40 4. let x = rate of the current let y = rate the man can row in still water going upstream against current = y-x = 500ft/10min = 50 ft/min going downstream with the help of current = y+x = 500ft/5min = 100 ft/min therefore y = 50+x substitution yields 50+x+x =100 solve yields x=25ft/min and y=75ft/min

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