Question

help me please i'm stuck Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Myra owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests. The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests. How many guests does each size of tier serve? A small tier will serve ? guests and a large tier will serve ? guests.

Answer 1

the number of guests a small tier can serve is 22

the number of guest a large tier serves is 40

Step-by-step explanation

Step 1

Set the equations

a) let

x represents the number of guest one small tier serves

y represents the number of guests one large tier serves

b) translate into math term

i)The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests,so

`3x+4y=226\Rightarrow equation(1)`

ii) The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests,so

`x+y=62\Rightarrow equation(2)`

Step 2

solve the equations:

a) isolate the x value in equation (2) and replace in equatino (1) to solve for y

`\begin{gathered} x+y=62\Rightarrow equation(2) \\ subtract\text{ y in both sides} \\ x=62-y \end{gathered}`

replace into equation(1) and solve for y

`\begin{gathered} 3x+4y=226\Rightarrow equation(1) \\ 3(62-y)+4y=226 \\ 186-3y+4y=226 \\ add\text{ like terms} \\ 186+y=226 \\ subtrac\text{ 186 in both sides} \\ 186+y-186=226-186 \\ y=40 \end{gathered}`

so, the number of guest a large tier serves is 40

b)now, replace the y value into equation (2) and solve for x

`\begin{gathered} x+y=62\Rightarrow equation(2) \\ x+40=62 \\ subtract\text{ 40 in both sides} \\ x+40-40=62-40 \\ x=22 \end{gathered}`

so, the number of guests a small tier can serve is 22the number of guests a small tier can serve is 22

I hope this helps you