Question

If three Magnums and two Paddlepops cost $8.70 and the difference in price between a Magnum and a Paddlepop is 90 cents, how much does each type of ice cream cost?

Answer 1

Answer:  Magnum = $2.10

               Paddlepop = $1.20

Step-by-step explanation:

Let M represent Magnum and P represent Paddlepop, then create a system of equations using the cost as one equation and the difference in price as the other.  Use the elimination method to solve for one of the variables and substitution to solve for the other.

3M + 2P = 8.70   →   1(3M + 2P = 8.70)   →   3M + 2P = 8.70

 M  -  P  = 0.90   →   2(M  -  P  = 0.90)    →   2M  - 2P = 1.80  

                                                                      5M         = 10.50

                                                                        M          =  2.10

 M  - P = 0.90

2.10 - P = 0.90

       -P = -1.20

        P = 1.20

Answer 2

Let the Magnum be represented by : M

Let the Paddlepop be represented by : P

Given : Three Magnums and Two Paddlepops cost $8.70

$:\implies$  3M + 2P = 8.70  ----------- [1]

Given : Difference between a Magnum and a Paddlepop is 90 cents

As 1 Dollar is made up of 100 cents, 90 cents can be written as $0.9

$:\implies$  M - P = 0.9

Multiplying above equation with 2, We get :

$:\implies$  2M - 2P = (2 × 0.9)

$:\implies$  2M - 2P = 1.8  ----------- [2]

Adding Equation [1] and [2], We get :

$:\implies$  3M + 2P + 2M - 2P = 8.70 + 1.8

$:\implies$  5M = 10.5

$:\implies$  M = 2.1

As the Difference between a Magnum and Paddlepop is $0.9

$:\implies$  2.1 - P = 0.9

$:\implies$  P = 2.1 - 0.9

$:\implies$  P = 1.2

Answers :

A Magnum Ice-cream costs : $2.1

A Paddlepop Ice-cream costs : $1.2