Johan has some boxes. He has only small boxes, medium boxes and large boxes. number of small boxes : number of medium boxes=2:5 number of medium boxes : number of large boxes=4:7 Johan has more than 150 boxes in total. What is the least possible number of large boxes that he could I have?

## Step1: Assess the RatioWe interpret the given ratio for number of small boxes: number of medium boxes: number of large boxes.Initially we are to assume , but from the text, it's clear that the number of medium boxes in both ratios aren't equal.## Step2: Equalize the RatiosTo match the number of medium boxes in both the ratios, we'll need to convert them into equivalent ratios. Therefore, we compute the least common multiple (LCM) of 5 and 4. ### Here, we adjust the 2 original ratios, as follows: ratio from Change it to: ratio from Change it to: This leads us to a corresponding ratio of small: medium: large as .## Step 3: Total up the Ratio PartsThe ratio can be simplified further by adding all of them together to determine the total number of 'parts' each ratio represents.\(Total parts = 8 (small boxes) + 20 (medium boxes) + 35 (large boxes) = 63 parts.\)## Step 4: Division of BoxesJohan has more than 150 boxes in total. And so, each part represents ### Being that a box can't be a fraction, we'll start from 3 boxes per part.## Step 5: Calculate Number of Large BoxesWe now determine the least number of large boxes present by multiplying the ratio for large boxes by 3 (number of boxes/ part),###