Use diagrams or the description of equivalent ratios to show that the ratios 2: 3, 4: 6, and 8: 12 are equivalent.

4:6 and 8:12 are equivalent ratios to 2:3 as you can see in the diagram below

4:6

_2_  _2_  

_2_  _2_  _2_  

8:12

_4_ _4_

_4_ _4_ _4_

Step-by-step explanation:

The diagrams of equivalent ratios represent the initial relation, in the image you can see each value is in a box so as the initial relation is 2:3 we have two boxes in the first row and three on the second. Now we have to find a number that added the times of the box, give us the other ratios 4:6 and 8:12

4:6

_2_  _2_  = 4

_2_  _2_  _2_    = 6

As 4 is 2 times 2 and 6 is 3 times 2, 4:6 is an equivalent ratio to 2:3 where 2 is the constant.

8:12

_4_ _4_ = 8

_4_ _4_ _4_ =12

As 8 is 2 times 4 and 6 is 3 times 4, 8:12 is an equivalent ratio to 2:3 where 4 is the constant.

To calculate the constant you may divide each of the corresponding values for example 4 divided by 2 is 2 and 6 divided by 3 is 2 then the constant for 4:6 is 2.

In the case of 8:12, 8 divided by 2 is 4 and 12 divided by 6 is 4 then the constan for 8:12 is 4

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

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step-by-step explanation: