Your friendshave been going to the local art studio and learning how to throw pottery. They have told you that there is a one time fee to join the studio and then a charge for each vessel you make. Heather paided $\$90$ when she made $5$ vessels and Terry was charged a total of $\$108$ when she made $8$ items. How much is the one time fee? How much does it cost to make each vessel?

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Multiply and divide decimals: word problems

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Q. Your friendshave been going to the local art studio and learning how to throw pottery. They have told you that there is a one time fee to join the studio and then a charge for each vessel you make. Heather paided

\$90

when she made

5

vessels and Terry was charged a total of

\$108

when she made

8

items. How much is the one time fee? How much does it cost to make each vessel?

Equations Setup: Let's denote the one-time fee as $F$ and the cost per vessel as $V$ . We can set up two equations based on the information given. Heather paid $\$90$ for $5$ vessels, and Terry paid $\$108$ for $8$ vessels. This gives us the following equations: $\newline$ $1$ ) $F + 5V = 90$ $\newline$ $2$ ) $F + 8V = 108$
Elimination Method: To find the values of $F$ and $V$ , we can use the method of elimination or substitution. Let's subtract the first equation from the second to eliminate $F$ and solve for $V$ . This will give us: $(F + 8V) - (F + 5V) = 108 - 90$
Solving for Cost per Vessel: Simplifying the equation, we get: $\newline$ $F + 8V - F - 5V = 108 - 90$ $\newline$ $8V - 5V = 18$ $\newline$ $3V = 18$
Substitute Cost per Vessel: Dividing both sides of the equation by $3$ to solve for $V$ , we get: $\newline$ $V = \frac{18}{3}$ $\newline$ $V = 6$ $\newline$ So, the cost to make each vessel is $\$6$ .
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Find One-Time Fee: Now that we know the cost per vessel, we can substitute $V$ back into one of the original equations to find the one-time fee $F$ . Let's use the first equation: $\newline$ $F + 5V = 90$ $\newline$ Substituting $V = 6$ into the equation, we get: $\newline$ $F + 5(6) = 90$ Solving for $F$ , we have: $\newline$ $F + 30 = 90$ $\newline$ $F = 90 - 30$ $\newline$ $F = 60$ $\newline$ So, the one-time fee is $\$60$ .