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Total all categories from a pictograph

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $7$ flowers each, and any leftover flowers will be wrapped one at a time. If $95\ \text{cm}$ of ribbon is needed to make one bouquet and $28\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(3 large pictures, 2 small pictures)
Tulip	(1 large picture, 5 small pictures)
Chrysanthemum	(2 large pictures, 1 small picture)
Lily	(1 large picture, 9 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Measurement & data

Your answer

How to solve

Strategy Identify Subproblems — Several steps chain together: read each flower count, find the grand total, divide by 7 for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

1STEP 1

Read each flower count from the pictograph

Each large picture is 10 and each small is 1. Rose: 3x10 + 2 = 32. Tulip: 1x10 + 5 = 15. Chrysanthemum: 2x10 + 1 = 21. Lily: 1x10 + 9 = 19.

32, 15, 21, 19

2STEP 2

Find the total number of flowers

Add all four counts: 32 + 15 + 21 + 19 = 87 flowers in all.

32 + 15 + 21 + 19 = 87

3STEP 3

Divide into bouquets of 7

Group 87 flowers by 7: 87 / 7 = 12 with remainder 3, so there are 12 bouquets and 3 single flowers left over.

87 ÷ 7 = 12 R 3

4STEP 4

Ribbon for bouquets and singles

12 bouquets x 95 cm = 1140 cm, and 3 singles x 28 cm = 84 cm. Add: 1140 + 84 = 1224 cm.

12 × 95 = 1140, 3 × 28 = 84, 1140 + 84 = 1224 cm

5STEP 5

Convert to meters and centimeters

Since 100 cm = 1 m, 1224 cm = 12 m and 24 cm left over.

1224 cm = 12 m 24 cm

Answer

12 m 24 cm (1224 cm)

1224 cm = 12 m 24 cm

87 flowers in groups of 7 give 12 bouquets (84 flowers) plus 3 singles = 87, which checks. Ribbon 1140 + 84 = 1224 cm, and 12 m 24 cm = 1224 cm, so the conversion is right; about 12 m is sensible for a dozen bouquets.

Takeaway

Count the flowers, group by 7, then add up the ribbon and trade every 100 cm for a meter!

Read each flower count from the pictograph
Find the total number of flowers
Divide into bouquets of 7
Ribbon for bouquets and singles
Convert to meters and centimeters

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