Together, dante and mia have a total of 350 pennies in their piggy banks. after dante lost ½ of his pennies and mia lost ⅓ of her pennies, they both had an equal number of pennies. altogether, how many pennies did they lose?

Together, Dante and Mia have a total of 350 pennies in their piggy banks. After Dante lost ½ of his pennies and Mia lost ⅓ of her pennies. Altogether, they lose  150 pennies.

Let the number of pennies Dante possess be equal to = x,

the number of pennies Mia possesses be equal to = y

Let assume the universal amount of pennies is 1

After Dante lost half of his pennies; he has 1 -  ½ = ½ pennies left

After Mia lost ⅓ of his pennies, she has 1 - ⅓ = ²/₃ pennies left

So, we can say:

From equation (1), let x be equal to 350 - y.

Then, we substitute the value of x into equation (2) to solve for y

∴

By cross multiply

3(350 -y) = 2(2y)

1050 - 3y = 4y

1050 = 4y + 3y

1050 = 7y

y = 150

From equation (1), since we know the value of y, we can easily determine the value of x by substituting the value of y into equation (1)

x + y = 350

x + 150 = 350

x = 350 - 150

x = 200

Now;

If Dante lost  ½ of his pennies, then it implies that Dante lost  ½ × 200 pennies = 100 pennies

If Mia lost ⅓ of her pennies, then Mia lost = ⅓ × 150

= 50 pennies

Therefore, we can conclude that the number of pennies they both lost altogether = (100 + 50)pennies = 150 pennies

Learn more about substitution here:

link