Question

Fund Raising. Suppose you have signed up for a bike-a-thon to raise money for charity. One person is sponsoring you at a rate of $0.50 per mile. Each of the other sponsors plans to donate $15 no matter how far your bike. a) Write a system of equations to model the donation d for m miles biked. b) For how many miles will all sponsors donate the same amount?

Answer 1

The system of equation is
`\left \{ {{d=15} \atop {d=0.5m}} \right.`.

After 30 miles all the sponsors donate the same amount.

Explanation:

Given:

Amount of donated by each of the other sponsors = $15

Amount donating by one person per mile = $0.5

We need to write the system of equation to model the donation d for m miles biked.

Also We need to find the number of miles all sponsors donate the same amount.

Solution:

Let the amount donated be denoted by 'd'.

Let number of miles biked be denoted by 'm'.

Now we know that;

Amount of donated by each of the other sponsors = $15

so we can say that;

`d=15`

Also We know that;

Amount donating by one person per mile = $0.5

So we can say that;

`d=0.5m`

Hence The system of equation is
`\left \{ {{d=15} \atop {d=0.5m}} \right.`.

Now to find the number of miles when all the sponsors donate the same amount we will make both the equation equal we get;

`0.5m=15`

Dividing both side by 0.5 we get;

`(0.5m)/(0.5)=(15)/(0.5)\\\\m=30\ miles`

Hence After 30 miles all the sponsors donate the same amount.