The larger of two integers is seven more than the smaller integer. their sum is 49. find the integers.

The two integers have values 28 and 21

Step-by-step explanation:

This is a simultaneous equation problem. Let the two integers be represented by and .

The first part of the question can be represented by the following equation:

From the second part of the question, we know their sum is 49, which can be represented by:

Now, we need to manipulate the expressions to contain just one unknown value. If we add to both sides of the first equation we get:

Now we can substitute the value of for in the second equation:

Which we can then rearrange and solve for :

We can now use the value for in either of the two original equations for find the value of :

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We now have the the two values 28 and 21.

Note: To double check the answer, check if their sum is equal to 49:

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ryan had a head start of 10 meters.