Question

63. Liv volunteered for h hours. Gavin volunteered for 4 fewer hours than Liv. Together they volunteered a total of 50 hours. Write an equation that could be used to find the total number of hours that the two teens worked.

64. Brendan rides his bike at a constant speed, s, for 0.75 hours. Write a formula that could be used to find the distance that he rides.

65. Alexis swam m meters and Sade swam half as many meters as Alexis. Together they swam a total of 200 meters. Write an equation that could be used to find the total number of meters that Alexis swam.

66. Grace ate five more peanuts than Keona. Grace ate g peanuts. Together they are 40 peanuts. Write an equation that could be used to find the number of peanuts that Grace ate.

Answer 1

Question 1:

For this case we have to:

h: Let the variable representing the amount of hours Liv was offered.

y: Let the variable representing the number of hours Gavin was offered.

According to the data we have to:

`h + y = 50\\y = h-4`

So, replacing the second equation in the first we have:

`h + (h-4) = 50\\h + h-4 = 50\\2h = 54`

With that equation we find the number of hours of Liv (
`h = 27 hours`) and then we find the number of hours of GAvin (
`y = 23 hours`)

ANswer:

`2h = 54`

Question 2:

For this case we have that by definition, the distance traveled is given by:

`x = v * t`

Where:

x: It is the distance traveled

v: It's the speed

t: It's time

According to the data we have to:

`v = s\\t = 0.75`

Substituting we have:

`x = 0.75s`

Answer:

`x = 0.75s`

Question 3:

For this case we have to:

m: Be the variable that represents the number of meters Alexis swam

y: Be the variable that represents the number of meters that Swim sade

According to we have to:

`m+y = 200\\y = \frac {m} {2}`

Substituting the second equation into the first we have:

`m +\frac {m} {2} = 200`

Thus, with the previous equation we can find the amount of meters that Alexis swam.

Answer:

`m +\frac {m} {2} = 200`

Question 4:

For this case we have to:

g: Let the variable representing the amount of peanuts Grace ate

y: Let the variable representing the amount of peanuts Kenoa ate

According to the data we have to:

`g + y = 40\\y + 5 = g`

According to the first equation we have to:

`y = 40-g`

If we substitute in the second equation:

`40-g + 5 = g\\45 = 2g`

Answer:

`45 = 2g`