On Monday Bob used 1 whole and-one half of a tank of gas to go on a college visit. On Tuesday he used five-eighths of a tank to commute to work. On Thursday, he went to the doctor and used of a tank less than one-third he used on Tuesday. On Saturday, he took his friends on a hiking trip and used of the three-fourths amount he used on his college visits. How much gas did Bob use overall last week
To find out how much gas Bob used overall last week, we need to add up the amounts of gas he used each day.
On Monday, he used 1 + 1/2 = 3/2 of a tank of gas.
On Tuesday, he used 5/8 of a tank of gas.
On Thursday, he used less than 1/3 of the tank he used on Tuesday, so we can say he used 1/3 - 1/x, where x is the amount of gas he used on Tuesday.
On Saturday, he used 1/2 * 3/4 = 3/8 of a tank of gas.
Now we need to find the value of x. We know that 1/3 - 1/x is the amount of gas he used on Thursday, and that is less than 1/3 of the tank he used on Tuesday. So we can write the inequality:
1/3 - 1/x < 1/3 * 5/8
Multiply both sides of the inequality by 8x:
8x * (1/3 - 1/x) < 8x * (1/3 * 5/8)
8x/3 - 8 < 5x/3
Let's combine like terms on the left side:
8x/3 - 5x/3 < 8
(8x - 5x)/3 < 8
3x/3 < 8
Simplify:
x < 8
So the amount of gas he used on Tuesday, x, must be less than 8.
Now we can add up all the amounts of gas to find out how much gas Bob used overall:
3/2 + 5/8 + 1/3 - 1/x + 3/8 = (48 + 15 + 16 - 8 - 9)/(24) = 62/24 = 2 and 14/24 = 2 and 7/12
Therefore, Bob used overall 2 and 7/12 of a tank of gas last week.