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Question

There are 180 blue and red cubes in a box. When the number of red cubes is decreased by 30% and the number of blue cubes is increased by 40%, there is now as many red as blue cubes in the box.     A) Is there an increase / decrease in the total number of cubes now? 

B) How many more / fewer cubes are in the box now?

 

 

 

Answer

This is a Simultaneous Equation.

70% = 7/10 = 14/20

140% = 14/10

     After    Transfer   Before   
Blue  14u +6u 20u  
Red  14u -4u 10u  
Total   28u   30u  

30u = 180

1u = 180 ÷ 30 = 6

2u = 2 × 6 = 12

a) Decrease

b) 12

 

 

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Before:  10B + 10R = 180                

After:      14B + 7R , 

and:        14B = 7R              —> 2B = 1R

Before:  10B + 10R = 180  —> 10B + 20B = 30B = 180  –> 1B = 180/30=6

After:      14B + 7R 

             = 14B + 14B

             = 28B (less than 30B, so decrease in total number of cubes# Ans for (a)

             = 180 – 2×6 = 168 cubes in total now (Updated: 12 lesser cubes now#) Ans for (b)

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Hi alfretztay, Unappreciated Teacher, SAHMom & Khong Pek Mao

Thank you so much for the answer 🙂

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(a)
red cubes : 1u
blue cubes : 1p

1u + 1p ——- 180
0.7u ——- 1.4p
7u ——- 14p
1u ——- 2p
2p + 1p = 3p ——- 180
1p ——- 180/3 = 60
1u ——- 2 x 60 = 120
0.7u ——- 84
84 x 2 = 168 (decrease)
(b)
180 – 168 = 12

Ans : (a) decrease; (b) 12 fewer cubes.

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