The cost of 1 apple and 5 mangoes is $6.15.
Let's look at how to form and solve simultaneous equations in a word problem.
<h3>State assumption and define variables:</h3>
Assuming that the cost of each apple and mango is equal in both packs.
Let the cost of an apple be a and that of a mango be m.
<h3>Write equations based on given information:</h3>
10a +5m= 12 -----(1)
15a +4m= 14.15 -----(2)
<h3>Solve by elimination:</h3>
<u>Steps for solving equations with two variables</u>
- Ensure that the magnitude of the coefficients of one of the term is equal in both equations
- Eliminate the term with the chosen term through subtraction or addition
- Solve for the other term
- Substitute the value of the term found in (3) to find the value of the second term
<u>Working</u>
Here, I am making the value of the coefficient of m constant.
(1) ×4:
40a +20m= 48 ----(3)
(2) ×5:
75a +20m= 70.75 -----(4)
Moving on to step 2, we can eliminate the m term by subtracting equation (3) from (4). When the sign of the terms are equal, we use subtraction to eliminate the term. On the other hand, if one of the sign is positive and the other is negative, adding the two equations together will eliminate the term (provided that you have already ensured that the magnitude of the coefficient is equal).
(4) -(3):
75a +20m -(40a +20m)= 70.75 -48
Expand:
75a +20m -40a -20m= 22.75
Simplify:
35a= 22.75
Let's continue with step 3, where we solve for a.
a= 22.75 ÷35
a= 0.65
The cost of an apple is $0.65.
Now, moving on to step 4!
Substitute a= 0.65 into (1):
10(0.65) +5m= 12
6.5 +5m= 12
5m= 12 -6.5
5m= 5.50
5 mangoes costs $5.50.
Cost of 1 apple and 5 mangoes
= $0.65 +$5.50
= $6.15
Thus, the cost of 1 apple and 5 mangoes is $6.15.
