Read the situation below and answer the questions that follow. Write your
answers on a separate sheet of paper.
Mr. Castillo makes small and large gift boxes to be sold during the Christmas
season. The materials for a small gift box costs P15 while the materials for a large
gift box costs P20. In a day, he has to finish making 6 boxes and spend only P110
for the materials.
Questions:
1. What equations can be used to model the situation?
2. How many small gift boxes and large gift boxes will he be able to finish in one
day?
RIGHT ANSWER MAY BRAINLIEST
Answers
Answer:
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Given: Mr. Castillo makes small and large gift boxes to be sold during the Christmas season. The materials for a small gift box costs P15 while the materials for a large gift box costs P20. In a day, he has to finish making 6 boxes and spend only P110 for the materials.
To find: 1- Equation to be used to model the situation
2- Number of small and large gift boxes he finishes in one day
Solution: Let the number of small boxes be x and the number of large boxes be y.
Total number of boxes to be made in a day= 6
Therefore, x+y = 6 ----equation(i)
The small box costs P15 and large box costs P20. He spends a total of P110 for making them.
Money used for making small boxes
= Money used for making 1 small box * Total small boxes
= 15x
Money used for making large boxes
= Money used for making 1 large box * Total large boxes
= 20y
Therefore, 15x+ 20y= 110----equation(ii)
These two equations can be solved to find the number of large and small gift boxes.
Multiplying equation (i) by 15 and subtracting it from equation (ii),
15x+20y- 15(x+y) = 110- 15×6
=> 15x + 20 y -15 x-15y = 110-90
=> 5y = 20
=> y= 4
Putting y= 4 in equation (i)
x + 4 = 6
=> x = 6-4
=> x = 2
Therefore, the number of small boxes and large boxes he finishes in one day are 2 and 4 respectively.