Hannah places her home on a grid so that each unit square on the grid equates to 11 mile. She uses the fact that the major stree
ts in her town are located 11 mile apart and run at right angles to each other to place her school 55 miles south and 33 miles east of her home.
The distance from Hannah's home to her school, if that distance could be walked in a straight line, would be _____ miles.
Enter your answer as the number that correctly fills in the blank in the previous sentence.
Round your answer to one decimal place, if necessary, like this: 42.5
The distance from Hannah's home to her school, if that distance could be walked in a straight line, would be _____ miles.
Enter your answer as the number that correctly fills in the blank in the previous sentence.
Round your answer to one decimal place, if necessary, like this: 42.5
1 answer:
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Let x be the number of bags of Nature's Recipe Venison Meal & Rice Canine 20 percent protein, y be the number of bags of Nutro Max Natural Dog Food 27 percent protein and z be the number of bags of PetSmart Premier Oven Baked Lamb 25 percent protein a dog breeder buys. He wants to make 300 pounds of a mix. Then
20x+17.5y+30z=300.
Now
- in 20x pounds of Nature's Recipe Venison Meal & Rice Canine 20 percent protein is 0.2·20x=4x pounds of protein;
- in 17.5y pounds of Nutro Max Natural Dog Food 27 percent protein is 0.27·17.5y=4.725y pounds of protein;
- in 30z pounds of PetSmart Premier Oven Baked Lamb 25 percent protein is 0.25·30z=7.5z pounds of protein;
- in 300 pounds of mix containing 22 percent protein is 0.22·300=66 pounds of protein.
Then 4x+4.725y+7.5z=66.
You get a system
From the first equation Substitute it into the second equation:
Simplify it:
y must be divided by 20, then
- y=0, x=9, z=10-6=4;
- y=20, x=16, z is not a whole number;
- y=40, x=23, z is not a whole number;
- y=60, x=30, z=10-20-35<0;
- thus, all other possible z will be <0.
Answer: 9 bags with 1st mix, 0 bags with 2nd mix and 4 bags with 3rd mix.