Question 1092935
<br>You want 13 pounds of candies.  So<br>
let x = pounds of orange slices, at $1.27 per pound
then 13-x = pounds of strawberry leaves, at $1.77 per pound<br>
The total cost of the 13 pounds of candies is $19.01:<br>
{{{1.27(x) + 1.77(13-x) = 19.01}}}
{{{1.27x + 23.01-1.77x = 19.01}}}
{{{-.5x = -4}}}
{{{x = 8}}}<br>
You need 8 pounds of orange slices and 13-8=5 pounds of strawberry slices.<br>
Now here is a way to solve this kind of problem without using algebra and all those ugly decimals.<br>
The cost of 13 pounds of strawberry leaves would be 13*1.77 = 23.01.
The cost of 13 pounds of orange leaves would be 13*1.27 = 16.51.
The actual cost of the 13 pounds of mixture is 19.01.<br>
Where the 19.01 lies (think of it on a number line) between 16.51 and 23.01 exactly determines the ratio in which the two kinds of candies need to be mixed.<br>
23.01-19.01 = 4.00;
19.01-16.51 = 2.50.<br>
Those two differences tell us that the two candies need to be mixed in the ratio 4.00:2.50, or 8:5.<br>
If there are 13 pounds of candies in the ratio 8:5, then there are 8 pounds of one and 5 pounds of the other.<br>
Since the cost of the mixture is closer to 16.51 than it is to 23.01, the larger amount of candy must be the less expensive kind.<br>
So you need 8 pounds of orange slices and 5 pounds of strawberry leaves.