Mox baked some mango, apple and peach tarts. There were 12 more mango tarts than peach forts and 20 more apple tarts than mango forts. He sold 3/8 of the apple tarts and 1/2 of the mango tarts. He had 145 tarts left. How many tarts did he sell altogether?

Answer 1

Let's start by using variables to represent the number of tarts.

Let M = number of mango tarts
Let A = number of apple tarts
Let P = number of peach tarts

From the problem, we know:

M = P + 12 (12 more mango tarts than peach tarts)
A = M + 20 (20 more apple tarts than mango tarts)

We also know that he sold 3/8 of the apple tarts and 1/2 of the mango tarts, so:

Number of apple tarts sold = 3/8A
Number of mango tarts sold = 1/2M

Finally, we know that he had 145 tarts left, so:

M + A + P = 145

Now we can use substitution to solve for the variables.

Substituting M = P + 12 and A = M + 20 into M + A + P = 145:

(P + 12) + (P + 12 + 20) + P = 145

Simplifying:

3P + 44 = 145

3P = 101

P = 33.67

Since we can't have a fraction of a tart, let's round up to 34 peach tarts.

Using M = P + 12:

M = 46

Using A = M + 20:

A = 66

Now we can calculate the number of tarts sold:

Number of apple tarts sold = 3/8A = 3/8(66) = 24.75

Number of mango tarts sold = 1/2M = 1/2(46) = 23

Again, we can't have a fraction of a tart, so let's round up to 25 mango tarts sold.

Altogether, he sold:

24 apple tarts + 25 mango tarts = 49 tarts.