13 plums weigh as much as 2 apples and 1 pear. 4 plums and 1 apple have the same weight as 1 pear. how many plums have the weight of 1 pear

Question

13 plums = 2 apples & 1 pear. 4 plums & 1 apple = 1 pear

 

Answer 1

13 plums=2 apples+1 pear

4 plums+1 apple=1 pear

substitute into the first equation

13 plums=2 apples+4 plums+1 apple

13 plums=3 apples+4 plums

13 plums-4 plums=3 apples

9 plums=3 apples

3 plums=1 apple

substitute into the second equation

4 plums+3 plums=1 pear

7 plums=1 pear

Answer 2

Let p = the number of plums

Let a = the number of apples

Lete r = the number of pears

 

13p = 2a + r

4p + a = r         Subtract 4p from both sides.

a = r - 4p          Substitute this equation into the 1st equation.

13p = 2(r-4p) + r   Use the distributive property.

13p = 2r - 8p + r    Add 8p to both sides and combine the r's.

21p = 3r                 Divide both sides by 3.

  7p = r