SOLUTION: you have been asked to contribute to a service project benefiting a local organization. you plan to buy a combination of $5 dollar and $10 gift cards to donate. You plan to buy exa

Question 1089840: you have been asked to contribute to a service project benefiting a local organization. you plan to buy a combination of $5 dollar and $10 gift cards to donate. You plan to buy exactly 20 gift cards and want to spend between $150 and $160. What are the possible combinations of $5 and $10 gift cards you can purchase? write a compound inequality in one variable to solve this problem
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.

Let x be the number of 10-dollar gift card.

Then the number of 5-dollar gift cards is (20-x).


The value of this combination is  10x + 5(20-x) dollars,  or  10x + 100 - 5x = 5x + 100 dollars.


According to the condition, this compound inequality must be in place

150 <= 5x + 100 <=160.


To solve it, subtract 100 from all three compounds of this inequality.  You will get an equivalent compound inequality

150 - 100 <= 5x <= 160 - 100,

or, which is the same

50 <= 5x <= 60.


Divide all the compounds by 5. You will get an equivalent compound inequality

10 <= x <= 12.


It is your answer: the number of 10-dollars gift cards is between 10 and 12.
                   
Then the number of 5-dollar gift card is between 8 and 10.


Answer. All possible combinations are 

         8  5-dollar cards and  12  10-dollar cards   (8*5  + 12*10 = 40 + 120 = 160);
         9  5-dollar cards and  11  10-dollar cards   (9*5  + 11*10 = 45 + 110 = 155);
        10  5-dollar cards and  10  10-dollar cards   (10*5 + 10*10 = 50 + 110 = 160).

Solved.

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