Algebra homework

Question

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 14 people took the trip. She was able to purchase coach tickets for ​$190 and first class tickets for

​$980. She used her total budget for airfare for the​ trip, which was ​$9770. How many first class tickets did she​ buy?

Answer 1

To solve his problem you need to set up 2 equations with 2 unknowns. The two unknowns are:

a = # of first class tickets

b = # of coach tickets

the first equation is that the number of first class tickets + coach tickets must add up to 14 total tickets:

EQ1: a+b = 14

the second equation is trickier but is the (number of first class tickets)*(price of a first class ticket) + (number of coach tickets)*(price of a coach ticket) = $9770:

EQ2: a*($980) + b*($190) = $9770

the rest of the problem can be solved many ways but one way is:

rearrange EQ1: b = 14 - a

plug in the rearranged equation in EQ2

a*($980)+ (14-a)*($190) = $9770

a*980-a*($190) + 2660 = $9770

solve for a:

a = 9

so 9 first class tickets were purchased

Answer 2

Let x be the number of first class tickets bought.

So, number of coach tickets bought = 14-x

Then the equation for total cost is =>

980x + 190(14-x) = 9770

980x + 2660 - 190x = 9770

790x = 7110

x=9

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An intuitive method might be, see how many times 980 will go in 9770. It goes 9.96 times. Take the whole number 9, and go forward if the rest adds up.

9770 - (980*9)=950. Divide 950 by 190, you get 5, and 9+5=14. So, number of first class tickets bought is 9.