Question

Julia has to mow two yards.She will need 13/16 gallon of gas to mow the first yard and 2/5 gallon to mow the second yard. She has 1 1/2 gallons of gas in her can. Does she have enough to mow both yards? Explain.

Answer 1

Julia has more than enough gas to mow both yards. She needs a combined total of 1 17/80 gallons, and she has 1 1/2 gallons, which is more than required.

Step-by-step explanation:

Julia needs to mow two yards, requiring 13/16 gallon of gas for the first yard and 2/5 gallon for the second. To determine if she has enough in her 1 1/2 gallons of gas, we need to add the amounts needed for both yards and compare the total to what she has.

First, let's convert 1 1/2 gallons to an improper fraction. This is 3/2 gallons when expressed as a fraction. Now to add the fractions:

• 
  
• 13/16 gallon + 2/5 gallon = (13*5)/(16*5) + (2*16)/(5*16) = 65/80 + 32/80 = 97/80 gallons

Now, convert 97/80 gallons to a mixed number to compare with what Julia has:

• 
  
• 97/80 = 1 17/80 gallons

Julia's 1 1/2 gallons, or 3/2 gallons, is equivalent to 120/80 gallons when expressed with the same denominator of 80. Thus:

• 
  
• 120/80 gallons > 97/80 gallons

Since 120/80 is greater than 97/80, Julia has more than enough gas to mow both yards.

Answer 2

Julia has enough gallons of gas to mow the two yards.

Step-by-step explanation:

Given:

Total yards Julia has to mow = 2

Gas in gallons required for the 1st yard =
`(13)/(16)`

Gas in gallons required for the 1st yard =
`(2)/(5)`

Gallons of gas Julia has =
`1(1)/(2)`.

To find if she has enough gas to mow the two yards.

Solution:

In order to find the total gas she would require to mow two yards, we will add the amounts of gas required for each yard.

Total amount of gas required to mow 2 yards is :

⇒ Gallons of gas required for 1st yard + Gallons of gas required for 2nd yard

⇒
`(13)/(16)+(2)/(5)`

To add fractions we will need take least common denominator between 16 and 5.

On comparing the multiples of 16 and 5, we find out the least common multiple is 80.

To make the denominators common, we will multiply the numerators and denominators with such a number that gives 80 as denominator.

So, we have:

⇒
`(13* 5)/(16* 5)+(2* 16)/(5* 16)`

⇒
`(65)/(80)+(32)/(80)`

Then, we add the numerators.

⇒
`(97)/(80)`

⇒ 1.21 gallons

Julia has
`1(1)/(2)` gallons of gas which is = 1.5 gallons.

Since 1.5>1.21, therefore we can say Julia has enough gallons of gas to mow the two yards.