Answer:
- $6400 at 13%, $3600 at 10.5%
- 82 hot dogs and 91 hamburgers
Explanation:
These are variations of a "mixture problem." A reasonable approach to the solution is to choose a variable to represent the quantity of the item contributing most to the mix. Then the quantity of the other item is the difference from the total quantity and the variable value. The equation you write will add up the values of the different quantities to get the total value.
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1.
Let x represent the amount invested at 13%. Then 10000-x is the amount invested at 10.5%, and the total interest earned is ...
0.13x +0.105(10000 -x) = 1210
0.025x +1050 = 1210 . . . . . eliminate parentheses
0.025x = 160 . . . . . . . . . subtract the constant on the left
x = 6400 . . . . . . . . . . divide by the coefficient of the variable
10000 -x = 3600
Anthony invested $6400 at 13% and $3600 at 10.5%.
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2.
Let x represent the number of burgers sold. Then the number of hot dogs sold is 173-x, and the total revenue is ...
3x +2(173 -x) = 437
x +346 = 437 . . . . . . . . . eliminate parentheses
x = 91 . . . . . . . . . . . . subtract the constant on the left
173 -x = 82
82 hot dogs and 91 hamburgers were sold.
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Additional comment
You can solve these by writing two equations in two unknowns. You would let the variables represent the quantities of the two contributors. You would have one equation for the total quantity, and another equation for the total value.
These equations can be solved in any of the usual ways. If you solve by "substitution," where you substitute for the quantity of lower value, the equation you have as a result will match the equation described above.
The reason for keeping the variable representing the larger contributor is that its coefficient ends up positive as the solution progresses. That tends to make the arithmetic a little simpler and to reduce errors.