The answers are;
A. 20 - x
B. 1500 - 50x
C. 1500 - 75x and 25x
In order to solve word problem leading to algebraic expression, the following steps should be taken.
Given that Jackson buys tickets for two concerts. The tickets for the concert featuring the local artist are $25 each. The tickets for the concert featuring the international artist are $75. Jackson buys a total of 20 tickets.
A. Let x be the number of tickets Jackson buys for the concert featuring the local artist. How many tickets does Jackson buy for the concert featuring the international artist?
The number of ticket Jackson buy for the concert featuring the international artist will be 20 - x
B. Write an algebraic expression to represent the total cost of both concerts for Jackson.
For both concert, the algebraic expression will be
25x + 75( 20 - x )
Open the bracket
25x + 1500 - 75x
Sum up the like terms
1500 - 50x
C. Interpret the parts of the expression by identifying how much Jackson pays for tickets for each of the two concerts
The algebraic expression 1500 - 50x means Jackson paid less than $1500 for both concert featuring the international artist and the local artist
For concert featuring the international artist, Jackson paid
1500 - 50x - 25x
1500 - 75x
For concert featuring the local artist, Jackson paid
1500 - 50x - 75( 20 - x )
1500 - 50x - 1500 + 75x
25x
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The algebraic expression to represent the total cost of both concerts for Jackson is 1875 - 50x
Let
number of tickets Jackson buy for the concert featuring the international artist = Total number of tickets - number of tickets Jackson buys for the concert featuring the local artist
= 20 - x
Algebraic expression for the total cost of both concerts for Jackson = 25(x) + 75(20-x)
= 25x + 1875 - 75x
= 1875 - 50x
Amount Jackson pays for tickets for each of the two concerts;
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