Question

A tour director collected $258 for 13 packages. Tour package A costs $18 and tour package B costs $22. How many pf each tour package were sold?

Answer 1

7 tour packages A and 6 tour packages B were sold.

Step-by-step explanation:

Given,

Total amount collected = $258

Total number of packages = 13

Cost of Package A = $18

Cost of Package B = $22

Let,

x represent the number of Package A.

y represent the number of Package B.

According to given statement;

x+y=13     Eqn 1

18x+22y=258    Eqn 2

Multiplying Eqn 1 by 18

$18(x+y=13)\\18x+18y=234\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(18x+22y)-(18x+18y)=258-234\\18x+22y-18x-18y=24\\4y=24$

Dividing both sides by 4

$\frac{4y}{4}=\frac{24}{4}\\y=6$

Putting y=6 in Eqn 1

$x+6=13\\x=13-6\\x=7$

7 tour packages A and 6 tour packages B were sold.

Keywords: linear equation, elimination method

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