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Hello I would appreciate if you could help me with this math question:

The number of Eric’s $5 to $10 was 3:2 at first. He used 1/5 of his $10 and some $5 notes to pay for a gift. The ratio of the number of $5 notes to $10 notes spent on the gift was 3:1. If the amount of $5 notes left was $360, how much did the gift cost?

 

Thank you:)

Answer

post-19668
0 Replies 2 Likes ✔Accepted Answer

ratio of $5 notes : $10 notes is 3 ; 2. We multiply five on both sides. The ratio of $5 notes to $10 notes will be 15 : 10. He used 1 unit of the $10 notes and 3 units of the $5 notes. Hence the ratio of $5 notes to $10 notes left will be 12:9.

Take $360/$5 = 72 pieces of $5 notes.

72/12 = 6 (1u)

6 x 10 = $60

3 x 6 x $5 = $90

total cost of gift will be $60+$90=$150

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The number of Eric’s $5 to $10 was 3:2 at first. He used 1/5 of his $10 and some $5 notes to pay for a gift. The ratio of the number of $5 notes to $10 notes spent on the gift was 3:1. If the amount of $5 notes left was $360, how much did the gift cost?

Value = 15 units (5*3): 20 Units (10*2)

4 Units * 3 = 12 Units 

12 Units / 2 = 6 Units

9 Units = 360

1 Unit = $40

Value of gift = 10 Units so cost = $400

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You will see below, I have use ratio in terms of value instead of number of notes. Just s simple conversion by multiplying the respective $dollar value to the ratio.

Ratio in value of what he had at first
$5 : $10 => 15u : 20u

Ratio in value of what he spent
$5 : $10 => 15p : 10p

We know he used 1/5 of $10 notes he had,
10p = 1/5 ( 20u) = 4u
1u = 10/4 (p)
15u = 37.5p , Substitute this is the equation below

He left $360 of $5 notes,
15u – 15p = 360
37.5p – 15p = 360
p = 16

Total he spent = 15p + 10p = 25p = $400 ##

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This is a Matrix question. We shall start with the cross ratio.

LCM
Spend     3 : 1 = 6 : 2

    Spend  Save   Total  
$5     6u 9u 15u
$10      2u 8u 10u

9u = 360
1u = 360 / 9 = 40
6u = 6 x 40 x $5 = $120
2u = 2 x 40 x $10 = $80
$120 + $80 = $200

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9u is not equal to $360
it is 9u X $5 = $360

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