Malik uses pennies to make three consecutive perfect squares. He uses 13 more pennies for the second square than for the first. Next he uses 15 more pennies for the third square than for the second. What is the total number of pennies he used to make three squares?

The total number of pennies Malik used to make the three squares is 149

Step-by-step explanation:

Let's recall that a perfect square of coins can be made of the same number of rows and columns, therefore:

x = Number of columns

x = Number of rows

Therefore,

x² + 13 = y

y has to be a whole number, which square root is also a whole number.

If x = 1, then y is 14 (1 + 13) and 14 is not a perfect square.

if x = 2, then y is 17 (4 + 13) and 17 is not a perfect square,

if x = 3, then y is 22 (9 + 13) and 22 is not a perfect square,

if x = 4, then y is 29 (16 + 13) and 29 is not a perfect square,

if x = 5, then y is 38 (25 + 13) and 38 is not a perfect square,

if x = 6, then y is 49 (36 + 13) and 49 is a perfect square because √49 is 7.

Now we need to calculate if the second condition is met:

if x = 6 and y = 7, then ײ + 28 = 64 (36 + 28) or y² + 15 = 64 (49 + 15) and 64 is also a perfect square because √64 is 8.

The total number of pennies Malik used to make the three squares is 36 + 49 + 64

The total number of pennies Malik used to make the three squares is 149.