On a map, the length from Cleveland to New York is 7 cm, from Cleveland to Atlanta is 10 cm, and from New York to Atlanta is 13 cm. If on a larger map the length from Cleveland to New York is 17.5 cm, what are the other lengths

Question

Mathematics

Vang

30 August, 18:29

On a map, the length from Cleveland to New York is 7 cm, from Cleveland to Atlanta is 10 cm, and from New York to Atlanta is 13 cm. If on a larger map the length from Cleveland to New York is 17.5 cm, what are the other lengths

+1

Answers (1)

Know the Answer?

Myles · Answer 1

Answer: Cleveland to Atlanta on the larger map is 25cm

New York to Atlanta on the larger map is 32.5 cm

Step-by-step explanation:

The length from Cleveland to New York is 7 cm on the smaller map. On a larger map the length from Cleveland to New York is 17.5 cm, this means the ratio of the length from Cleveland to New york on the smaller map to the length on the larger map is 7/17.5

Let x = the length from Cleveland to Atlanta on the larger map.

Let y = the length from New York to Atlanta on the larger map.

The length from Cleveland to Atlanta on the smaller map is 10 cm, it means that the ratio of the length from Cleveland to Atlanta on the smaller map to the length on the larger map is 10/x

The length from New York to Atlanta on the smaller map is 13 cm. it means that the ratio of the length from New York to Atlanta on the smaller map to the length on the larger map is 13/y

The ratios are the same because the maps are similar. Therefore,

7/17.5 = 10/x = 13/y

To find x,

7/17.5 = 10/x

7x = 17.5 * 10 = 175

x = 175/7 = 25 cm

To find y

10/x = 13/y

10/25 = 13/y

10y = 25*13 = 325

y = 325/10 = 32.5. cm