QuestionMike and Hugo share money in a $3:5$ ratio. If Mike gets \$18, what is the total amount?

Studdy Solution

STEP 1

Assumptions1. Mike and Hugo share a sum of money in the ratio $35$ . . Mike gets $\$18$ .
3. The total sum of money is divided according to the given ratio.

STEP 2

First, we need to understand that the ratio $5$ means that for every $$ parts that Mike gets, Hugo gets $5$ parts. This ratio can be used to find the total sum of money.

STEP 3

We know that Mike's share corresponds to $3$ parts of the total sum. So, we can find the value of one part by dividing Mike's share by $3$ .
$Value\, of\, one\, part = Mike's\, share /3$

STEP 4

Now, plug in the given value for Mike's share to calculate the value of one part.
$Value\, of\, one\, part = \$18 /3$

STEP 5

Calculate the value of one part.
$Value\, of\, one\, part = \$18 /3 = \$$

STEP 6

Now that we have the value of one part, we can find the total sum of money. This is done by multiplying the value of one part by the total number of parts in the ratio (3 parts for Mike plus5 parts for Hugo).
$Total\, sum\, of\, money = Value\, of\, one\, part \\times Total\, number\, of\, parts$

STEP 7

Plug in the values for the value of one part and the total number of parts to calculate the total sum of money.
$Total\, sum\, of\, money = \$6 \\times (3 +5)$

STEP 8

Calculate the total sum of money.
$Total\, sum\, of\, money = \$6 \\times8 = \$48$ The total sum of money is $\$48$ .

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