Question

Madelyn and her friend Beth are each baking apple pies and tarts for a bake sale, using the same recipes. Madelyn baked 1 apple pie and 3 apple tarts, using a total of 19 apples. Beth made 10 apple pies and 10 apple tarts, which used 110 apples. How many apples does each dessert require?

An apple pie uses ____ apples and an apple tart requires____apples.

Answer 1

• Apple pie be x
• Apple tart be y

The equations are

• x+3y=19--(1)
• 10x+10y=110=>x+y=11---(2)

Subtracting both equations

`\\ \sf\longmapsto 2y=8`

`\\ \sf\longmapsto y=4`

Put in equation (2)

`\\ \sf\longmapsto x+4=11`

`\\ \sf\longmapsto x=7`

Answer 2

• An apple pie uses 7 apples and an apple tart requires 4 apples

Explanation:

Apple pie - p, apple tart - t

Set the system as follows:

• p + 3t = 19
• 10p + 10t = 110

Solve by substitution, p = 19 - 3t:

• 10(19 - 3t) + 10t = 110
• 190 - 30t + 10t = 110
• 20t = 190 - 110
• 20t = 80
• t = 4

Find the value of p:

• p = 19 - 3*4 = 19 - 12 = 7