Algebraic Calculations For Various Scenarios
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1. Two of the top-grossing concert tours were by a jazz and a rock band. Together the two tours visited 185 cities. The jazz band visited 99 cities more than the rock band. How many cities did the jazz band visit? how many cities did the rock band visit?
2. A baseball team has home games on Friday and Saturday. The two games together earn $3634.00 for the team. Fridays game generates $566.00 less than Saturdays game. How much money was taken in at each game? Friday? Saturday?
3. A motel clerk counts his $1 and $10 bills at the end of the day. He finds he has a total of 46 bills having a combined monetary value of $181. How many ones? How many tens?
4. A boat crew rowed 12 miles downstream, with the current, on 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 4 hours. Find the crews rowing rate in still water and the rate of the current. Rowing rate in still water? Rate of the current?
5. Soybean meal is 18% protein, cornmean is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 15% protein?
How many pounds of cornmean? How many pounds of soybean?
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Solution Summary
This is a set of solutions to word problems leading to simultaneous equations, the problems are drawn from a number of different scenarios
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1. Let the number of cities visited by the jazz band be j, and that by the rock band be r, then
j+r=185 ___________(1) [Together the two tours visited 185 cities]
j-r=99 ____________(2) [The jazz band visited 99 cities more than the rock band]
making j subject of the formula in equation (1) gives
j=185-r ___________(3)
and making j subject of the formula in equation (2) gives
j=99+r ___________(4)
we can now equate the right hand sides of equations (3) and (4) since they are both equal to j:
185-r=99+r
collecting like terms:
185-99=r+r
86=2r
Therefore, r=86/2 =43
substituting r=43 in equation (3) gives
j=185-43 =142
Answer: j=142 and r=43;
meaning that the jazz band visited 142 cities while the rock band visited 43 cities.
2. Let the amount taken at the Friday game be $f and at the Saturday game be $s, then
f+s=3634 ___________(1) [The two games together earn $3634.00 for the team]
s-f=566 ____________(2) [Fridays game generates $566.00 less than saturdays game]
making s subject of the formula in equation (1) gives
s=3634-f ___________(3)
and making s subject of the formula in equation (2) gives
s=566+f ...
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