Math Kangaroo (Benjamin) 2014 Problem No 24

Try this beautiful Problem based on simple Algebra appeared in Math Kangaroo (Benjamin) 2014 Problem 24.

Math Kangaroo (Benjamin) 2014 | Problem No 24

Grandma gives 180 marbles to her ten grandchildren. No two children get the same amount of marbles. Anna gets the most. What is the minimum number of marbles that Anna could get?

Key Concepts

Arithmetic

Equation solving

Algebra

Suggested Book | Source | Answer

Algebra by Gelfand

Math Kangaroo (Benjamin), 2014

$23$

Try with Hints

Here

Number of children is $10$.
Number of marbles is $180$.
And Anna gets the most and no 2 children gets the same number of marbles.

Let us assume that Anna could get $x$ marbles and also the other 9 children receiving 1 less each step. Apply the condition to construct the equation

The equation will be-

$x$+$x$-$1$+$x$-$2$+$x$-$3$+$x$-$4$+$x$-$5$+$x$-$6$+$x$-$7$+$x$-$8$+$x$-$9$=$180$

Now solve for $x$.

So, Anna can have $23$ marbles.

Math Kangaroo (Benjamin) 2021 Problem No 22

Try this beautiful Problem based on simple Arithmetic appeared in Math Kangaroo (Benjamin) - 2021.

Math Kangaroo (Benjamin) 2021 | Problem No 22

Maurice asked the canteen chef for the recipe for his pancakes. Maurice has 6 eggs, $400 \mathrm{~g}$ flour, 0,5 liters of milk and $200 \mathrm{~g}$ butter. What is the largest number of pancakes he can make using this recipe?

Key Concepts

Arithmetic

Division

Multiplication

Suggested Book | Source | Answer

Algebra by Gelfand

Arithmetic | Math Kangaroo (Benjamin), 2021

$8$

Try with Hints

For $100$ pancakes we need -

$25$ eggs
$4$ Litres milk
$5 kg$ flour
$1 kg$ butter.

Now calculate for one pancake how much ingredient is needed?

For one pancake we need,

$0.25$ egg

$0.04$ Litres milk

$0.05 kg$ flour

$0.01 kg$ butter.

Calculate how many pancakes can be made with each ingredients available.

With $6$ eggs we can have $24$ pancakes.

With $400 g$ flour we can have $8$ pancakes.

With $0.5 $ Litres milk we can have $12.5$ pancakes.

With $200 g$ butter we can have $20$ pancakes.

Compare the number of pancakes for each ingredient to make the pancake complete.

So, we can have $8$ pancakes complete.

Math Kangaroo (Benjamin) 2014 Problem No 24