# Question

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:)

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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