Each pen costs 3 times as much as each eraser. If the total cost of 2 pens and 4 erasers is $6.30, find the cost of each pen.
Let's call the cost of each eraser "x".
Then according to the problem, each pen costs 3 times as much, so the cost of each pen is 3x.
We are told that the total cost of 2 pens and 4 erasers is $6.30, so we can set up an equation:
2(3x) + 4x = 6.30
Simplifying this equation:
6x + 4x = 6.30
10x = 6.30
x = 0.63
So each eraser costs $0.63.
To find the cost of each pen, we can use our earlier equation:
Each pen costs 3 times as much as each eraser, so:
3x = 3(0.63) = 1.89
Therefore, each pen costs $1.89.
Some grapes are shared between Mary and Lincoln in the ration 4:5. If Lincoln receives 0.31kg more grapes than Mary, how many kilograms of grapes does Mary recieve?
Let's call the amount of grapes Mary receives "4x".
According to the problem, Lincoln receives 0.31kg more grapes than Mary, so Lincoln receives "4x + 0.31".
The total amount of grapes shared is the sum of what Mary and Lincoln receives:
4x + (4x + 0.31) = 8x + 0.31
We know that the grapes were shared in the ratio of 4:5, so we can write:
5/9(8x + 0.31) = amount of grapes Lincoln receives
4/9(8x + 0.31) = amount of grapes Mary receives
We want to find the amount of grapes Mary receives, so we can simplify the last equation:
4/9(8x + 0.31) = 4x
Multiplying both sides by 9 to get rid of the denominator:
4(8x + 0.31) = 36x
Simplifying and solving for x:
32x + 1.24 = 36x
1.24 = 4x
x = 0.31
So Mary receives 4x = 4(0.31) = 1.24kg of grapes.
If Kenny spends $4 a day, his money will last for 3 weeks. If he spends $2.75 a day, how much will be left after 3 weeks?
Let's start by finding out how much money Kenny has for 3 weeks if he spends $4 a day.
There are 7 days in a week, so in 3 weeks there are 7 x 3 = 21 days.
If Kenny spends $4 a day for 21 days, then he spends:
$4/day x 21 days = $84
Now let's find out how much money he has left if he spends $2.75 a day for 21 days.
He spends $2.75 a day for 21 days:
$2.75/day x 21 days = $57.75
To find out how much he has left, we need to subtract the amount he spent from the total amount he had:
$84 - $57.75 = $26.25
Therefore, Kenny has $26.25 left after 3 weeks if he spends $2.75 a day.
The average height of 3 boys and 4 girls is 1.29m. If the average height of the 3 boys is 1.33m, find the average height of the 4 girls.
Let's first find the total height of the 3 boys.
The average height of the 3 boys is 1.33m, so their total height is:
1.33m x 3 = 3.99m
Now let's find the total height of all 7 children.
If the average height of 3 boys and 4 girls is 1.29m, then their total height is:
1.29m x 7 = 9.03m
We can use this information to find the total height of the 4 girls:
Total height of all 7 children - Total height of 3 boys = Total height of 4 girls
9.03m - 3.99m = 5.04m
So the total height of the 4 girls is 5.04m.
To find the average height of the 4 girls, we divide by 4:
Average height of 4 girls = 5.04m ÷ 4 = 1.26m
Therefore, the average height of the 4 girls is 1.26m.