Answer:
27 miles
28 miles
Step-by-step explanation:
so, on the first map 6 cm on the map are 36 miles in real life.
the trail is 4.5 cm on the map.
therefore, we need to multiply the ratio 6/36 on top and bottom with the same factor (so that the ratio value remains unchanged).
which factor ? the factor that turns 6 into 4.5.
6×x = 4.5
x = 4.5/6
so, we have
6/36 × (4.5/6)/(4.5/6) = (6×4.5/6) / (36×4.5/6) =
= 4.5 / (6×4.5)
so, 4.5 cm on the map are 6×4.5 = 27 miles in real life.
in this case we could also make it faster :
the ratio 6/36 can be simplified to 1/6.
so, 1 cm on the map is 6 miles in real life.
now we see directly, that we only need to multiply this 1/6 ratio to and bottom by 4.5 (to get the 4.5 cm on the map) and we get
4.5 / (6×4.5) = 4.5 / 27
on the second map we have the ratio 3/24. that can Amado be simplified to 1/8.
we need 3.5 cm, so we need to multiply top and bottom by 3.5
1/8 × 3.5/3.5 = 3.5 / (8×3.5) = 3.5 / 28
so, that trail is 28 miles long.
for the general solution (if we cannot simplify the original ratio to 1/n) again, we need to turn 3 into 3.5.
what factor does this ?
3×x = 3.5
x = 3.5/3
so, we have
3/24 × (3.5/3)/(3.5/3) = (3×3.5/3) / (24×3.5/3) =
= 3.5 / (8×3.5)
therefore 3.5 cm on the map correlate to 8×3.5 = 28 miles in real life.
