Question

A truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1:4:3 if there are 76 tomato juice bottles, then how many juice bottles in total are there?

Answer 1

Answer: Total number of juice bottles is 152

The truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1 : 4: 3

There are 76 tomato juice bottle

Let the number of grapefruit bottle = x

Let the number of pineapple juice bottle = y

1: 4 : 3 = x : 76: y

To find the number of juice bottles, we will need to establish a proportion

`\begin{gathered} 1\text{ : 4 = x : 76} \\ (1)/(4)\text{ = }(x)/(76) \\ \text{Introduce cross multiply} \\ 1\cdot\text{ 76 = 4 }\cdot\text{ x} \\ 76\text{ = 4x} \\ \text{Divide both sides by 4} \\ (76)/(4)\text{ = }(4x)/(4) \\ x\text{ = }(76)/(4) \\ x\text{ = 19} \end{gathered}`

To calculate for y, we will still need to establish a proportion

`\begin{gathered} 4\text{ : 3 = 76 : y} \\ (4)/(3)\text{ = }(76)/(y) \\ \text{Introduce cross multiply} \\ 4\cdot\text{ y = 76 x 3} \\ 4y\text{ = 228} \\ \text{Divide both sides by 4} \\ (4y)/(4)\text{ = }(228)/(4) \\ y\text{ = }(228)/(4) \\ y\text{ = 57} \end{gathered}`

Since, x is the number of grapefruit bottles, then the number of grapefruit bottles in the truck is 19 bottles

Since, y is the number of pineapple bottles, therefore, the number of pineapple bottle is 57 bottles

Total number of juice bottles in the lorry = 19 + 76 + 57

The total number = 152 juice bottles