If you are making a scale drawing of a giraffe that is 6 m tall, and the height of the giraffe in your drawing is 3 cm, what is the scale of the drawing?
The scale of the drawing can be determined by comparing the ratio of the actual height to the height in the drawing.
If the actual height of the giraffe is 6 m and the height in the drawing is 3 cm, we need to convert the measurements to the same units.
To convert 6 m to cm, we multiply by 100 since there are 100 cm in 1 m:
6 m * 100 cm/m = 600 cm
Now we can compare the actual height to the height in the drawing:
600 cm : 3 cm
To simplify the ratio, we divide both parts by the greatest common divisor, which is 3:
600 cm ÷ 3 = 200 cm
3 cm ÷ 3 = 1 cm
The simplified ratio is:
200 cm : 1 cm
Therefore, the scale of the drawing is 200 cm:1 cm, or simply 200:1.
S puts only dimes and quarters in his piggy bank. Right now, he has five more dimes than quarters in it and the total is $74.35. How many quarters and how many dimes are in Steve's piggy bank?
Let's assume the number of quarters in Steve's piggy bank is q.
Since there are five more dimes than quarters, the number of dimes would be q + 5.
To convert the number of quarters and dimes into dollars, we'll multiply the number of quarters by $0.25 (since one quarter is $0.25) and the number of dimes by $0.10 (since one dime is $0.10).
Therefore, the equation based on the given information would be:
0.25q + 0.10(q + 5) = 74.35
Simplifying the equation:
0.25q + 0.10q + 0.50 = 74.35
0.35q + 0.50 = 74.35
0.35q = 73.85
q = 73.85 / 0.35
q ≈ 211
So, the number of quarters in Steve's piggy bank is approximately 211.
Substituting the value of q into the equation for the number of dimes:
dimes = q + 5
dimes = 211 + 5
dimes = 216
Therefore, there are approximately 216 dimes in Steve's piggy bank.
J and JA went biking. JA biked for 5 1/3 hours at an average speed of 12 1/2 miles per hour. J traveled 1 1/5 times as far as JA did. How long was J's trip?
To find the length of J's trip, we need to determine the distance traveled by JA first.
JA biked for 5 1/3 hours at an average speed of 12 1/2 miles per hour. We can convert the mixed number into an improper fraction:
5 1/3 = (3 * 5 + 1) / 3 = 16/3
Now we can calculate the distance traveled by JA:
distance = speed * time
distance = (12 1/2) * (16/3) = (25/2) * (16/3) = 400/6 = 66 2/3 miles
J traveled 1 1/5 times as far as JA did. We can calculate J's distance by multiplying JA's distance by 1 1/5:
distance_J = (6/5) * (66 2/3)
To simplify the calculations, we can convert 66 2/3 into an improper fraction:
66 2/3 = (3 * 66 + 2) / 3 = 200/3
distance_J = (6/5) * (200/3) = (6/5) * (200/3) = (6 * 200) / (5 * 3) = 1200 / 15 = 80 miles
Therefore, J's trip was 80 miles long.